C₂⁷×C₃² #11770645

order	1152
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7864799660605440
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²¹×C₃

Aliases

C₂⁷×C₃²

175272 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 1152

A minimal faithful permutation representation — 7 generators on 20 points:

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

1152 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4656);