C₁₃×#10517 #15696856

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10517

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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)(16,24)(17,22)(18,21)(19,23)(20,26)(25,29)(27,28)(30,31,35,39)(32,40,43,55)(33,44,47,37)(34,48,50,38)(36,49,52,42)(41,57,45,56)(46,54,61,59)(51,58,53,60);(14,16)(15,20)(17,26)(18,27)(19,25)(21,29)(22,24)(23,28)(30,32,35,43)(31,36,39,52)(33,45,47,41)(34,49,50,42)(37,53,44,51)(38,55,48,40)(46,58,61,60)(54,56,59,57);(15,21)(16,25)(18,19)(22,23)(26,27)(28,29)(30,33,34,46,35,47,50,61)(31,37,38,54,39,44,48,59)(32,41,42,58,43,45,49,60)(36,51,40,56,52,53,55,57)

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, 3505);