C₁₃×#13346 #15699685

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13343
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₁₃
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃ ◁ C₂²×D₄×C₁₃ ◁ G

1022 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6334);