C₁₃×#11536 #15697875

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#11536

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 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

376 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 106 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)(14,15,17,19,18,20,16,21)(22,23)(24,32,35,47)(25,29)(26,39,41,30)(27,31)(28,34)(33,48,36,50)(37,52,53,45)(38,46)(40,43)(42,49)(44,51);(22,24,27,35)(23,28,31,43)(25,36,38,33)(26,40,41,34)(29,44,46,42)(30,47,39,32)(37,49,53,51)(45,48,52,50);(14,16,18,17)(15,19,20,21)(22,25,27,38)(23,29,31,46)(24,33,35,36)(26,37,41,53)(28,42,43,44)(30,45,39,52)(32,48,47,50)(34,49,40,51)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4524);