C₂×C₅²×C₂₇ #13062472

order	1350
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₂×C₅²×C₂₇

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1350

A minimal faithful permutation representation — 2 generators on 39 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)

1350 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1350, 31);