C₁₃×#12877 #15699216

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11669
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12877

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#418
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1824
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

366 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26,29,21)(17,31)(18,35)(19,41)(20,23)(22,33)(24,39)(25,38)(27,54,55,73)(28,58,36,68)(30,45,60,53)(32,63)(34,66)(37,51)(40,67)(42,50)(43,56,52,65)(44,61,49,70)(46,71)(47,64)(48,72)(57,75,62,77)(59,74,69,76);(14,16)(15,21)(17,27)(18,36)(19,30)(20,29)(22,43)(23,26)(24,49)(25,45)(28,40)(31,54)(32,55)(33,65)(34,57)(35,58)(37,69)(38,60)(39,70)(41,53)(42,62)(44,48)(46,74)(47,52)(50,77)(51,76)(56,64)(59,71)(61,72)(63,73)(66,75)(67,68);(14,17,19,42,20,32,38,34)(15,22,41,46,23,47,25,51)(16,27,30,62,29,55,60,57)(18,37,39,33,40,71,72,64)(21,43,53,74,26,52,45,76)(24,50,67,63,48,66,35,31)(28,59,61,56,36,69,70,65)(44,75,58,54,49,77,68,73)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5865);