C₁₃×#10391 #15696730

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10390
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#10391

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 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)(16,20)(17,28,30,21)(18,22)(19,24)(23,32)(25,40,29,37)(26,35)(27,36)(31,38,44,39)(33,41,45,43)(34,42);(14,16)(15,20)(17,29,30,25)(18,27)(19,26)(21,37,28,40)(22,36)(23,34)(24,35)(31,43,44,41)(32,42)(33,38,45,39);(14,17,19,31)(15,21,24,39)(16,25,26,41)(18,30,32,44)(20,33,35,37)(22,28,23,38)(27,29,42,43)(34,40,36,45)

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, 3379);