C₁₃×#12840 #15699179

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12026
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12840

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#427
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1808
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₁₃×M₁₆ ◁ C₂×C₁₃×#131 ◁ G

354 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 154 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)(14,15,19,26,21,25,20,42)(16,27,31,54,33,53,32,63)(17,34,36,49,37,23,41,48)(18,38,39,50,40,69,28,24)(22,43,46,61,45,55,52,30)(29,57,59,75,60,51,62,74)(35,66,56,65,67,68,70,47)(44,71,72,58,64,76,73,77);(14,16,28,55,20,32,40,61,21,33,39,43,19,31,18,30)(15,22,38,54,26,46,50,53,25,45,69,63,42,52,24,27)(17,29,56,76,36,59,67,77,37,60,70,71,41,62,35,58)(23,44,68,75,49,73,65,57,34,64,66,74,48,72,47,51);(14,17)(15,23)(16,29)(18,35)(19,41)(20,36)(21,37)(22,44)(24,47)(25,34)(26,49)(27,51)(28,56)(30,58)(31,62)(32,59)(33,60)(38,68)(39,70)(40,67)(42,48)(43,71)(45,64)(46,73)(50,65)(52,72)(53,57)(54,75)(55,76)(61,77)(63,74)(66,69)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5828);