C₁₃×#13667 #15700006

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13667
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13667

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₁₃×M₃₂ ◁ G

294 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 74 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)(15,20)(16,24)(17,27)(18,30)(21,33)(22,36)(23,37)(25,29)(26,38)(28,43)(31,42)(32,34)(35,44)(39,40)(41,45);(14,15)(16,25)(17,29)(18,32)(19,21)(20,24)(22,27)(23,30)(26,41)(28,44)(31,45)(33,38)(34,43)(35,42)(36,39)(37,40);(16,26)(20,33)(24,38)(25,41)(28,39)(34,37)(36,44)(40,43)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6655);