C₁₃×#13447 #15699786

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13447

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2054
prime radical	C₁₃×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 386 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) = 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)(16,29)(17,35)(18,42)(19,45)(20,25)(21,47)(22,28)(23,31)(24,38)(26,44)(27,43)(30,49)(32,59)(33,51)(34,58)(36,60)(37,68)(39,57)(40,71)(41,65)(46,53)(48,50)(52,64)(54,66)(55,69)(56,70)(61,73)(62,76)(63,75)(67,77)(72,74);(14,16)(15,23)(17,36)(18,32)(19,46)(20,31)(21,48)(22,34)(24,54)(25,50)(26,58)(27,59)(28,53)(29,42)(30,39)(33,43)(35,49)(37,62)(38,63)(40,61)(41,67)(44,64)(45,51)(47,52)(55,76)(56,77)(57,73)(60,68)(65,75)(66,69)(70,72)(71,74);(14,17,18,37,43,69,19,38,22,41,44,70,21,40,20,39)(15,24,25,55,47,68,26,35,28,57,45,71,27,56,42,65)(16,30,31,61,48,72,64,67,34,63,46,66,33,62,32,36)(23,49,29,60,59,76,51,54,53,75,58,77,52,74,50,73)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6435);