C₄×#126 #2304

order	128
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 12288
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

258 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1036);