C₄³×C₂₅ #13098523

order	1600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1720320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

C₄³×C₂₅

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₂³×C₅	C₂³×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

387 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4)(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);(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, 875);