C₁₃×#7166 #15693505

order	3328
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#7166

Subgroups

	subgroup	G/H
center	C₄²×C₁₃	C₂²⋊C₄
commutator	C₂×C₄	C₄×C₈×C₁₃
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃
socle	C₂²×C₁₃	#336
prime radical	C₂³×C₁₃	C₄⋊C₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

216 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,20)(19,21)(22,23,25,31,28,24,29,33,27,30,26,36,35,32,37,34);(15,18,20,19)(22,24,26,33,28,30,37,36,27,32,25,34,35,23,29,31)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 154);