C₁₃×#11914 #15698253

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11914

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1530
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#97	C₂³×C₁₃
prime radical	C₂³×C₁₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,15,18,24,19,25,39,55,20,26,38,56,41,23,50,52)(16,27,29,58,30,21,42,44,31,45,63,53,40,46,36,69)(17,32,34,64,35,49,67,54,33,51,37,71,65,22,47,48)(28,43,60,73,61,72,70,76,59,74,62,75,68,57,66,77);(14,16,20,31)(15,21,26,46)(17,28,33,59)(18,36,38,42)(19,40,41,30)(22,43,49,74)(23,45,25,27)(24,53,56,58)(29,39,63,50)(32,57,51,72)(34,66,37,70)(35,68,65,61)(44,52,69,55)(47,60,67,62)(48,76,54,77)(64,73,71,75);(14,17,20,33)(15,22)(16,28,31,59)(18,37,38,34)(19,35,41,65)(21,43)(23,51)(24,54)(25,32)(26,49)(27,57)(29,62,63,60)(30,61,40,68)(36,70,42,66)(39,47,50,67)(44,75)(45,72)(46,74)(48,56)(52,64)(53,77)(55,71)(58,76)(69,73)

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, 4902);