C₁₃×#11835 #15698174

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11799
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11835

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

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

normal subgroups only

This group has 340 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.

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)(15,19)(16,17)(20,21)(22,23,26,31,27,30,39,46)(24,32,34,47,35,28,40,42)(25,29,37,45,38,44,50,53)(33,43,48,52,36,41,49,51);(14,15)(16,19)(17,21)(18,20)(22,24,27,35)(23,28,30,32)(25,36,38,33)(26,34,39,40)(29,43,44,41)(31,47,46,42)(37,49,50,48)(45,51,53,52);(14,16,18,17)(15,19,20,21)(22,25,27,38)(23,29,30,44)(24,33,35,36)(26,37,39,50)(28,41,32,43)(31,45,46,53)(34,48,40,49)(42,51,47,52)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4823);