C₃²×C₃₇ #66528

order	333
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₄×C₉×GL(2,𝔽₃) (order 1728) · Inn(G) = C₁ · Out(G) = C₄×C₉×GL(2,𝔽₃)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₃₇

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 333

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(4,5,6)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(333, 5);