C₁₃×#23900 #15710239

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23900
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁸

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

3520 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 208

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 16888);