C₁₃×#32874 #15719213

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32873
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₃×#32874

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2840
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂⁴×C₁₃ ◁ G

688 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 186 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)(17,28)(18,22)(19,23)(20,27)(21,30)(25,34)(26,37)(29,42)(31,36)(32,39)(33,41)(35,43)(38,45)(40,44);(14,16)(15,20,23,24)(17,25)(18,26)(19,27)(21,34,28,32)(22,33,36,37)(29,40)(30,39)(31,41)(35,44,42,45)(38,43);(14,17)(15,21,23,28)(16,25)(18,29)(19,30)(20,32,24,34)(22,35,36,42)(26,40)(27,39)(31,43)(33,45,37,44)(38,41);(14,18,19,31)(15,22,23,36)(16,26,27,41)(17,29,30,43)(20,33,24,37)(21,35,28,42)(25,38,39,40)(32,44,34,45)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25862);