C₂×#13852 #514019

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

7282 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 22 points:

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

maximal subgroup of	C₂×#607927, C₂×#609004, C₂×#514522, …
maximal normal subgroup of	C₂×#607927, C₂×#609004, C₂×#514522, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421215);