C₁₃×#13444 #15699783

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

Aliases

direct product

C₁₃×#13444

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2054
prime radical	C₁₃×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 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)(16,17)(18,31)(19,39)(20,41)(21,26)(22,27)(23,33)(24,38)(25,37)(28,43)(29,45)(30,35)(32,36)(34,42)(40,44);(14,16)(15,22)(17,31)(18,36)(19,23)(20,42)(21,30)(24,34)(25,32)(26,43)(27,38)(28,40)(29,37)(33,41)(35,39)(44,45);(14,17,18,32,37,45,40,43,21,35,19,33,20,34,38,22)(15,23,24,30,41,28,39,29,26,36,44,16,25,27,31,42)

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, 6432);