C₁₃×#10669 #15697008

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#10669

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#399
prime radical	C₂³×C₁₃	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 296 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) = 61
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20,19,23,17,22)(16,24,26,29,27,28,25,21)(30,31,36,40,35,41,34,39)(32,42,50,37,45,53,44,52)(33,38,48,57,49,56,47,55)(43,58,46,61,60,54,59,51);(15,20)(16,25)(17,18)(21,29)(22,23)(26,27)(30,32,34,50,35,45,36,44)(31,37,39,53,41,52,40,42)(33,46,47,60,49,59,48,43)(38,54,55,51,56,58,57,61);(14,16,19,27)(15,21,23,29)(17,26,18,25)(20,28,22,24)(30,33,35,49)(31,38,41,56)(32,43,45,60)(34,47,36,48)(37,51,52,61)(39,55,40,57)(42,54,53,58)(44,59,50,46)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3657);