C₁₃×#13678 #15700017

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13677
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13678

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2196
commutator, Frattini, cosocle	#124	C₂³×C₁₃
LCS	G ▷ #124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#124 ◁ G

400 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 58 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)(17,28)(21,37)(22,36)(23,40)(24,29)(25,42)(26,32)(31,33)(35,38)(39,43)(41,45);(14,15)(16,21)(17,29)(18,23)(19,24)(20,28)(22,34)(25,43)(26,38)(27,39)(30,45)(31,40)(32,41)(33,36)(35,44)(37,42);(14,16,19,27)(15,21,24,39)(17,30,28,44)(18,32,34,26)(20,35,29,45)(22,38,23,41)(25,33,42,31)(36,37,40,43)

Conjugacy classes & character table

286 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6666);