C₁₃×#32898 #15719237

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁹

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

4360 conjugacy classes of subgroups; only the 370 normal subgroups are shown.

normal subgroups only

This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 370 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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)(14,15)(16,17)(22,25);(18,19)(20,22)(21,23)(24,25);(18,20)(19,22)(21,24)(23,25);(15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25886);