Linear representation theory of maximal unipotent subgroup of symplectic group of degree six over a finite field
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Contents |
This article gives specific information, namely, linear representation theory, about a family of groups, namely: maximal unipotent subgroup of symplectic group of degree six. This article restricts attention to the case where the underlying ring is a finite field.
View linear representation theory of group families | View other specific information about maximal unipotent subgroup of symplectic group of degree six | View other specific information about group families for rings of the type finite field
Summary
Item | Value |
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number of conjugacy classes (equals number of irreducible representations over a splitting field) | Case even (i.e., a power of 2): PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] Case odd: See number of irreducible representations equals number of conjugacy classes, element structure of maximal unipotent subgroup of symplectic group of degree six over a finite field |
degrees of irreducible representations over a splitting field (such as or ) | Case even (i.e., a power of 2): PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] Case odd: 1 (occurs times), (occurs times), (occurs times), (occurs times) |
sum of squares of degrees of irreducible representations | (equals order of the group) see sum of squares of degrees of irreducible representations equals order of group |
lcm of degrees of irreducible representations | |
condition for a field (characteristic not equal to ) to be a splitting field | PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] |
field generated by character values, which in this case also coincides with the unique minimal splitting field (characteristic zero) | PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] |
unique minimal splitting field (characteristic ) | PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] |