C₁₃×#9976 #15696315

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#9976

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

716 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 102 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)(22,23,28,32)(24,33,37,45)(25,38,42,48)(26,43,27,31)(29,36,46,35)(30,40,49,41)(34,51,52,44)(39,50,53,47);(18,21)(22,24)(23,29)(25,39)(26,36)(27,35)(28,37)(30,47)(31,45)(32,46)(33,43)(34,40)(38,44)(41,52)(42,53)(48,51)(49,50);(14,16)(15,18)(17,20)(19,21)(22,25,28,42)(23,30,32,49)(24,34,37,52)(26,40,27,41)(29,44,46,51)(31,48,43,38)(33,50,45,47)(35,39,36,53)

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, 2964);