C₂×C₄×#124 #34032

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 2097152
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

1895 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27020);