C₂×C₃×C₉×C₂₇ #13090164

order	1458
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1417176
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃²×C₉

Aliases

C₂×C₃×C₉×C₂₇

404 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1458

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29);(30,31,32,33,34,35,36,37,38);(39,40,41)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 238);