Element structure of extraspecial groups

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This article gives specific information, namely, element structure, about a family of groups, namely: extraspecial group.
View element structure of group families | View other specific information about extraspecial group

This article describes the element structure of extraspecial groups. An extraspecial group of order p^{1 + 2m}, with m \ge 1 and p a prime number, is a non-abelian group P of that order such that [P,P] = Z(P) = \Phi(P) is a cyclic subgroup of order p. We can deduce from this that the quotient group is an elementary abelian group of order p^{2m}.

For every prime p and every fixed m, there are two isomorphism classes of extraspecial groups of order p^{1+2m}, known as the extraspecial group of '+' and '-' type respectively.

Summary

Item Value
conjugacy class sizes size 1 (p times), size p (p^{2m} - 1 times)
number of conjugacy classes p^{2m} + p - 1
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]