order	128
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×#23794 (order 512) · Inn(G) = C₁ · Out(G) = C₂×#23794
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

C₄×C₃₂

Subgroups

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(33,34,35,36)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 128);