C₁₃×#13657 #15699996

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13657
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13657

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2177
commutator	C₁₆	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₁₃×#508	C₂²
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₁₃×#346 ◁ G

182 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 82 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)(16,28,31,62)(17,25)(18,36)(19,42)(20,45)(21,27)(22,30,48,69)(23,34)(24,39)(26,44)(29,64,66,77)(32,71,46,63)(33,72)(35,57)(37,56,65,61)(38,54)(40,51)(41,59)(43,60,68,52)(47,75,49,76)(50,74,58,70)(53,73)(55,67);(14,16)(15,22)(17,29)(18,37)(19,43)(20,46)(21,31)(23,47)(24,52)(25,56)(26,58)(27,48)(28,59)(30,67)(32,44)(33,70)(34,68)(35,66)(36,62)(38,74)(39,69)(40,76)(41,65)(42,49)(45,50)(51,71)(53,63)(54,64)(55,60)(57,61)(72,77)(73,75);(14,17,20,34,21,35,44,19)(15,23,26,25,27,42,45,57)(16,29,46,68,31,66,32,43)(18,38,40,39,41,33,73,67)(22,47,58,56,48,49,50,61)(24,53,54,59,55,51,72,36)(28,60,71,77,62,52,63,64)(30,37,74,76,69,65,70,75)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6645);