C₁₃×#13309 #15699648

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13309

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1999
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

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

normal subgroups only

This group has 568 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) = 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)(16,24)(17,28)(18,33)(19,22)(20,25)(21,31)(23,30)(26,40)(27,42)(29,39)(32,43)(34,37)(35,41)(36,44)(38,45);(14,16)(15,20)(17,29)(18,34)(19,26)(21,37)(22,35)(23,39)(24,28)(25,31)(27,30)(32,44)(33,36)(38,42)(40,43)(41,45);(20,35)(24,40)(36,39)(37,42)

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, 6297);