C₂⁴×C₄×C₂₇ #13145353

order	1728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 185794560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂⁴×C₄×C₂₇

2724 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1728

A minimal faithful permutation representation — 5 generators on 39 points:

(1,2,3,4)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(5,6);(7,8);(9,10);(11,12)

1728 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 11416);