C₃²×#3968 #13084955

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

Hall	C₃²×C₅ ⋊ #101
Sylow	C₅ ⋊ C₃²×#101

228 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3)(7,8,10,11,9)(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25);(4,5,6)(8,9)(10,11)(12,13,15,18,16,19,24,27)(14,20,21,26,22,17,23,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1272);