Element structure 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.
View linear representation theory of group families | View other specific information about maximal unipotent subgroup of symplectic group of degree six

Summary


Item Value
number of conjugacy classes Case q even (i.e., a power of 2): PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
Case q odd: q^4 + 4q^3 - 2q^2 - 3q + 1
equals number of irreducible representations. See number of irreducible representations equals number of conjugacy classes, linear representation theory of maximal unipotent subgroup of symplectic group of degree six over a finite field
order q^9
Follows from the general formula, order of maximal unipotent subgroup of Sp(n,q) is q^{n^2/4} = q^{6^2/4} = q^9
conjugacy class sizes Case q even (i.e., a power of 2): PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
Case q odd: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]