C₂×#1935 #21084

order	256
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

603 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14072);