C₂×#12590 #492912

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₆ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

1018 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 30 points:

(1,2);(7,8)(9,12)(10,11)(13,14)(15,16,17,20,18,21,23,26,19,22,24,27,25,28,29,30);(3,4,5,6)(8,11)(12,14);(7,9,10,13)(8,12,11,14)

320 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂×#126531, C₂×#93249, #72210358, …
maximal normal subgroup of	C₂×#126531, C₂×#93249, #72210358, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400108);