C₁₃×#8495 #15694834

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#8495

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

620 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 142 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)(15,19,21,24)(20,28,29,27)(30,31)(32,40,43,36)(33,44,46,53)(34,39)(35,38)(37,45,51,47)(41,56)(42,55,60,50)(48,52)(49,57)(54,59)(58,61);(14,15)(16,20)(17,24)(18,21)(19,26)(22,27)(23,29)(25,28)(30,32,35,43)(31,36,38,40)(33,41,46,58)(34,42,48,60)(37,49,51,54)(39,50,52,55)(44,61,53,56)(45,57,47,59);(14,16,18,23)(15,20,21,29)(17,25,26,22)(19,27,24,28)(30,33)(31,37)(32,41)(34,47)(35,46)(36,49)(38,51)(39,53)(40,54)(42,59)(43,58)(44,52)(45,48)(50,56)(55,61)(57,60)

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, 1483);