C₁₃×#12684 #15699023

order	3328
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#12684

Subgroups

	subgroup	G/H
center	C₈×C₁₃	#120
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1779
prime radical	C₁₃×#585	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

894 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 210 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)(14,15,18,23,19,24,33,43,20,25,34,44,35,45,56,66)(16,21,28,38,29,39,52,62,27,37,50,60,51,61,71,75)(17,22,31,41,32,42,55,65,30,40,53,63,54,64,72,76)(26,46,48,67,49,68,70,77,47,36,57,58,69,59,73,74);(14,16)(15,21)(17,26)(18,28)(19,29)(20,27)(22,36)(23,38)(24,39)(25,37)(30,47)(31,48)(32,49)(33,52)(34,50)(35,51)(40,46)(41,58)(42,59)(43,62)(44,60)(45,61)(53,57)(54,69)(55,70)(56,71)(63,67)(64,68)(65,74)(66,75)(72,73)(76,77);(14,17)(15,22)(16,26)(18,31)(19,32)(20,30)(21,36)(23,41)(24,42)(25,40)(27,47)(28,48)(29,49)(33,55)(34,53)(35,54)(37,46)(38,58)(39,59)(43,65)(44,63)(45,64)(50,57)(51,69)(52,70)(56,72)(60,67)(61,68)(62,74)(66,76)(71,73)(75,77)

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5672);