C₂⁶×C₂₅ #13103253

order	1600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 403174195200
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂⁶×C₂₅

8475 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 6 generators on 37 points:

(1,2)(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);(3,4);(5,6);(7,8);(9,10);(11,12)

1600 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5605);