C₁₃×#10529 #15696868

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10524
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10529

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#124
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 1664

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3517);