C₁₃×#13545 #15699884

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13545
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13545

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2101
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,15,18,23,19,21,31,38)(16,24,34,37,26,20,28,41)(17,29,32,45,33,22,30,40)(25,39,27,36,43,35,44,42);(14,16)(15,20,21,24)(17,25)(18,34)(19,26)(22,39,29,35)(23,41,38,37)(27,32)(28,31)(30,44)(33,43)(36,45,42,40);(15,21)(16,25,26,43)(17,30)(18,31)(20,35,24,39)(22,40)(27,34,44,28)(29,45)(32,33)(36,37,42,41)

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, 6533);