C₂×#367 #2157

order	128
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 889);