C₁₃×#13520 #15699859

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13520

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2087
prime radical	C₂³×C₁₃	C₂×Q₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 238 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,36,47,65,74,20,24,38,48,19,25,37,49)(16,21,27,41,55,70,75,77,28,43,56,72,29,42,57,71)(17,30,33,50,39,66,64,44,32,59,62,45,34,46,35,22)(26,51,52,73,58,76,63,67,31,60,61,68,53,69,54,40);(14,16)(15,21)(17,31,32,26)(18,27)(19,29)(20,28)(22,40,44,67)(23,41)(24,43)(25,42)(30,51,59,60)(33,61,62,52)(34,58,39,53)(35,63,64,54)(36,55)(37,57)(38,56)(45,68,50,73)(46,69,66,76)(47,70)(48,72)(49,71)(65,75)(74,77);(14,17,19,39,20,32,36,34)(15,22,25,50,24,44,47,45)(16,26,29,58,28,31,55,53)(18,35,37,33,38,64,65,62)(21,40,42,73,43,67,70,68)(23,46,49,30,48,66,74,59)(27,54,57,52,56,63,75,61)(41,69,71,51,72,76,77,60)

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, 6508);