C₁₃×#24412 #15710751

order	3328
nilpotency class	3
isoclinism	isoclinic class of #24412
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

1710 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 17400);