C₁₃×#12118 #15698457

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12117
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12118

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₁₃×#2017	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×M₁₆ ◁ G

392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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)(17,33)(18,37)(19,26)(20,25)(21,27)(22,30)(23,35)(24,40)(29,57)(31,65)(32,56)(34,68)(36,53)(38,46)(39,49)(41,54)(42,50)(43,52)(44,51)(45,72)(47,63)(48,64)(55,59)(58,66)(60,77)(61,75)(62,73)(67,71)(69,74)(70,76);(14,16,21,32)(15,22,27,48)(17,29,36,61)(18,38,41,63)(19,31,20,44)(23,45,50,74)(24,51,52,65)(25,47,26,46)(28,54,56,37)(30,43,64,40)(33,66,53,73)(34,69,39,72)(35,59,42,60)(49,75,68,57)(55,76,77,67)(58,70,62,71);(14,17)(15,23)(16,29)(18,39)(19,42)(20,35)(21,36)(22,45)(24,49)(25,53)(26,33)(27,50)(28,55)(30,62)(31,60)(32,61)(34,41)(37,67)(38,72)(40,70)(43,71)(44,59)(46,66)(47,73)(48,74)(51,75)(52,68)(54,76)(56,77)(57,65)(58,64)(63,69)

Conjugacy classes & character table

325 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5106);