C₂²×C₃⁴×C₅ #13108571

order	1620
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 582266880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃⁶

Aliases

C₂²×C₃⁴×C₅

2120 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1620

A minimal faithful permutation representation — 4 generators on 21 points:

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

1620 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 477);