C₁₃×#13373 #15699712

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13373

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2023
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25,27,42)(17,30)(18,23)(19,35)(20,24)(21,28,37,44)(22,34)(26,43,29,39)(31,41)(32,40,45,36)(33,38);(16,26,27,29)(17,31)(21,36,37,40)(22,38)(25,39,42,43)(28,45,44,32)(30,41)(33,34);(14,16)(15,21)(17,32)(18,29)(19,26)(20,27)(22,39)(23,40)(24,37)(25,41)(28,33)(30,42)(31,45)(34,44)(35,36)(38,43)

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, 6361);