C₁₃×#9190 #15695529

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9183
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9190

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

436 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 53
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18,19,20)(22,23,27,31,28,32,26,42)(24,33,37,44,36,48,35,29)(25,38,40,46,41,30,39,45)(34,47,51,43,50,53,49,52);(14,15,16,20,17,19,21,18)(22,24,28,36)(23,29)(25,34,41,50)(26,35,27,37)(30,43)(31,33)(32,44)(38,52)(39,49,40,51)(42,48)(45,53)(46,47);(22,25,28,41)(23,30,32,38)(24,34,36,50)(26,40,27,39)(29,43,44,52)(31,46,42,45)(33,47,48,53)(35,51,37,49)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2178);