C₄×#1784 #354798

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

3874 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);(5,6)(7,8)(9,10,12,16,13,15,21,23)(11,17,18,24,19,14,20,22);(9,11,13,19)(10,14,15,17)(12,20,21,18)(16,24,23,22);(6,8)

maximal subgroup of	#72266600, #72266601, #72266604, …
maximal normal subgroup of	#72266600, #72266601, #72266604, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261994);