C₁₃×#10121 #15696460

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10121

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#3153	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 544 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)(15,18)(16,20)(19,21)(22,23)(24,33)(25,38)(26,43)(27,31)(28,32)(29,35)(30,41)(34,51)(36,46)(37,45)(39,50)(40,49)(42,48)(44,52)(47,53);(16,20)(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);(14,15)(16,21)(17,19)(18,20)(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

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3109);