C₂×C₅²×C₂₅ #11929360

order	1250
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6000000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅³

Aliases

C₂×C₅²×C₂₅

240 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1250

A minimal faithful permutation representation — 3 generators on 37 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)

1250 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1250, 11);