C₁₃×#10630 #15696969

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#10630

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#397
prime radical	C₂³×C₁₃	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 61
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,20)(18,21)(22,29)(23,27)(24,26)(25,28)(30,31)(32,40,43,53)(33,37)(34,38)(35,39)(36,42,50,47)(41,56,44,55)(45,51)(46,52)(48,54)(49,58,60,57)(59,61);(14,16,17,23)(15,19,20,27)(18,22,25,24)(21,29,28,26)(30,32)(31,36)(33,44)(34,47)(35,43)(37,49)(38,53)(39,50)(40,54)(41,46)(42,48)(45,57)(51,56)(52,60)(55,61)(58,59);(15,20)(16,22)(18,25)(19,26)(23,24)(27,29)(30,33,34,45,35,46,48,59)(31,37,38,51,39,52,54,61)(32,41,42,57,43,44,47,58)(36,49,40,55,50,60,53,56)

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, 3618);