C₁₃×#11859 #15698198

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11859

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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)(16,22,24,19)(17,20)(18,21)(23,28,25,27)(26,29)(30,31)(32,42)(33,39)(34,49)(35,51)(36,41)(37,44)(38,47)(40,50)(43,59)(45,53)(46,56)(48,58)(52,57)(54,61)(55,60);(14,16)(15,19)(17,25)(18,24)(20,28)(21,22)(23,26)(27,29)(30,32,36,46)(31,37,41,55)(33,44,48,60)(34,43,47,61)(35,52,50,45)(38,56,49,42)(39,57,58,53)(40,59,51,54);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,33,35,47,36,48,50,34)(31,38,40,39,41,49,51,58)(32,43,45,60,46,61,52,44)(37,53,54,42,55,57,59,56)

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, 4847);