C₁₃×#9991 #15696330

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#9991

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 53
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,19)(20,21)(22,23,28,33)(24,34,38,45)(25,39,43,48)(26,32,27,31)(29,37,46,36)(30,41,49,42)(35,44,51,52)(40,53,50,47);(18,21)(22,24,28,38)(23,29,33,46)(25,40,43,50)(26,37,27,36)(30,47,49,53)(31,45,32,34)(35,42,51,41)(39,52,48,44);(14,16)(15,18)(17,20)(19,21)(22,25,28,43)(23,30,33,49)(24,35,38,51)(26,41,27,42)(29,44,46,52)(31,48,32,39)(34,47,45,53)(36,40,37,50)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2979);