C₁₃×#23896 #15710235

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₃×#23896

Subgroups

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

1764 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1764 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)(16,20)(17,21)(18,22)(19,23)(24,30)(25,31)(26,32)(27,40)(28,35)(29,36)(33,38)(34,41)(37,44)(39,43)(42,45);(14,16,19,26)(15,20,23,32)(17,24,28,38)(18,25,29,39)(21,33,35,30)(22,31,36,43)(27,37,41,45)(34,44,40,42);(14,17)(15,21)(16,24)(18,27)(19,28)(20,30)(22,34)(23,35)(25,37)(26,38)(29,41)(31,42)(32,33)(36,40)(39,45)(43,44);(14,18)(15,22)(16,25)(17,27)(19,29)(20,31)(21,34)(23,36)(24,37)(26,39)(28,41)(30,42)(32,43)(33,44)(35,40)(38,45)

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, 16884);