C₄×#1383 #146338

order	512
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

712 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 24 points:

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

maximal subgroup of	#72215297, C₄×#12647, #72216468, …
maximal normal subgroup of	#72215297, C₄×#12647, #72216468, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 53534);