C₂×C₃²×C₉² #13090341

order	1458
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1224440064
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁵×C₉

Aliases

C₂×C₃²×C₉²

2132 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1458

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2)(3,4,5,6,7,8,9,10,11);(12,13,14,15,16,17,18,19,20);(21,22,23);(24,25,26)

1458 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 415);