C₁₃×#23899 #15710238

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23897
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₃×#23899

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 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 — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,21)(18,30)(19,23)(20,27)(22,33)(25,41)(26,38)(28,39)(29,37)(31,34)(32,36)(35,43)(40,42)(44,45);(20,34)(24,38)(35,45)(40,41);(14,16)(15,20)(17,25)(18,31)(19,26)(21,35)(22,38)(23,34)(24,30)(27,33)(28,44)(29,42)(32,43)(36,40)(37,45)(39,41);(14,17,19,29)(15,21,23,37)(16,25,26,42)(18,32,33,28)(20,35,34,45)(22,39,30,36)(24,40,38,41)(27,44,31,43)

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, 16887);