C₂⁵×C₅×C₇ #11765486

order	1120
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 239984640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂⁵×C₅×C₇

1496 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1120

A minimal faithful permutation representation — 5 generators on 22 points:

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

1120 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 1092);