D₄×#341 #356488

order	512
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

2126 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 24 points:

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

maximal subgroup of	D₄×#1810, D₄×#1765, D₄×#1938
maximal normal subgroup of	D₄×#1810, D₄×#1765, D₄×#1938

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 263684);