C₈×#108 #8292

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

187 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,5,4,6,7,8);(9,10,13,16,14,17,12,22)(11,18,20,23,21,24,19,15);(9,11,12,19,14,21,13,20)(10,15,16,18,17,23,22,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 1280);