C₁₃×#33983 #15720322

order	3328
nilpotency class	5
isoclinism	isoclinic class of #33982
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#33983

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₁₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₁₃×#41 ◁ C₁₃×#131 ◁ C₁₃×#504 ◁ G

462 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 202 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 — 4 generators on 77 points:

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

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 26971);