C₂³×C₅×C₇² #14520047

order	1960
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1354752
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₇

Aliases

C₂³×C₅×C₇²

320 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2)(7,8,9,10,11)(12,13,14,15,16,17,18);(3,4)(19,20,21,22,23,24,25);(5,6)

1960 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 144);