C₂×#13755 #513338

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄²

Aliases

5594 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂×#608390, C₂×D₄×#376, C₂×#514280, …
maximal normal subgroup of	C₂×#608390, C₂×D₄×#376, C₂×#514280, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420534);