C₁₃×#9982 #15696321

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#9982

Subgroups

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

722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 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)(24,34,37,45)(25,30,41,48)(26,32,27,31)(29,38,44,36)(35,50,51,46)(39,53,52,43)(40,49,42,47);(18,21)(22,24)(23,29)(25,39)(26,38)(27,36)(28,37)(30,46)(31,45)(32,34)(33,44)(35,40)(41,52)(42,51)(43,47)(48,50)(49,53);(14,16)(15,18)(17,20)(19,21)(22,25,28,41)(23,30,33,48)(24,35,37,51)(26,40,27,42)(29,43,44,53)(31,47,32,49)(34,46,45,50)(36,39,38,52)

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, 2970);