C₁₃×#13075 #15699414

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13075

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

458 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 146 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)(17,32,34,22)(18,36)(19,41)(20,24)(21,29)(23,39)(25,38)(27,49)(28,50,57,70)(30,53)(31,63)(33,66,37,68)(35,47,67,65)(40,42)(43,56,64,59)(44,54)(45,61)(46,55,48,69)(51,62)(52,60)(58,76,75,72)(71,77,73,74);(14,16,27,54,19,31,18,29,20,30,39,62,38,60,40,61)(15,21,42,63,25,44,23,26,24,45,36,52,41,51,49,53)(17,28,55,74,35,58,37,59,34,57,69,77,67,75,33,56)(22,43,68,76,47,71,48,50,32,64,66,72,65,73,46,70);(14,17)(15,22)(16,28)(18,37)(19,35)(20,34)(21,43)(23,48)(24,32)(25,47)(26,50)(27,55)(29,59)(30,57)(31,58)(33,40)(36,66)(38,67)(39,69)(41,65)(42,68)(44,71)(45,64)(46,49)(51,73)(52,72)(53,70)(54,74)(56,61)(60,75)(62,77)(63,76)

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, 6063);