Element structure of extraspecial groups
This article gives specific information, namely, element structure, about a family of groups, namely: extraspecial group.
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This article describes the element structure of extraspecial groups. An extraspecial group of order , with and a prime number, is a non-abelian group of that order such that is a cyclic subgroup of order . We can deduce from this that the quotient group is an elementary abelian group of order .
For every prime and every fixed , there are two isomorphism classes of extraspecial groups of order , known as the extraspecial group of '+' and '-' type respectively.
Contents
Summary
Item | Value |
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conjugacy class sizes | size 1 ( times), size ( times) |
number of conjugacy classes | See also number of irreducible representations equals number of conjugacy classes, linear representation theory of extraspecial groups |
order statistics | depends on whether it's a + or - type; PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] |