C₂×#341 #1737

order	128
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

196 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 469);