C₁₃×#13312 #15699651

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13312

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1999
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

520 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 114 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)(16,28)(17,34)(18,39)(19,26)(20,25)(21,27)(22,30)(23,37)(24,42)(29,58)(31,64)(32,52)(33,57)(35,67)(36,69)(38,50)(40,55)(41,54)(43,53)(44,51)(45,74)(46,62)(47,63)(48,59)(49,72)(56,60)(61,77)(65,68)(66,71)(70,75)(73,76);(14,16)(15,22)(17,35)(18,40)(19,31)(20,32)(21,33)(23,48)(24,52)(25,46)(26,55)(27,47)(28,39)(29,37)(30,42)(34,65)(36,70)(38,60)(41,63)(43,62)(44,61)(45,50)(49,56)(51,75)(53,57)(54,64)(58,66)(59,72)(67,69)(68,71)(73,74)(76,77);(14,17)(15,23)(16,29)(18,36)(19,44)(20,37)(21,38)(22,45)(24,49)(25,50)(26,34)(27,51)(28,56)(30,59)(31,35)(32,60)(33,61)(39,66)(40,68)(41,73)(42,71)(43,72)(46,75)(47,65)(48,55)(52,77)(53,76)(54,69)(57,67)(58,64)(62,74)(63,70)

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, 6300);