C₁₃×#33981 #15720320

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

Aliases

direct product

C₁₃×#33981

Subgroups

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

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

normal subgroups only

This group has 466 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)(16,27)(17,23)(18,36)(19,40)(20,22)(21,29)(24,38)(25,34)(26,35)(28,55)(30,60)(31,62)(32,54)(33,63)(37,52)(39,68)(41,50)(42,49)(43,59)(44,56)(45,70)(46,72)(47,67)(48,65)(51,76)(53,58)(57,74)(61,77)(64,73)(66,69)(71,75);(14,16)(15,21)(17,28)(18,37)(19,41)(20,32)(22,43)(23,44)(24,50)(25,52)(26,53)(27,36)(29,38)(30,34)(31,35)(33,64)(39,71)(40,45)(42,57)(46,74)(47,75)(48,60)(49,73)(51,77)(54,68)(55,63)(56,65)(58,76)(59,72)(61,67)(62,69)(66,70);(15,22)(21,43)(23,26)(24,46)(25,47)(27,54)(36,68)(40,49)(44,53)(45,73)(48,51)(50,74)(52,75)(55,62)(60,77)(63,69);(14,17,20,35)(15,23,22,26)(16,28,32,31)(18,33,39,66)(19,34,42,67)(21,44,43,53)(24,48,46,51)(25,49,47,40)(27,55,54,62)(29,56,59,58)(30,57,61,41)(36,63,68,69)(37,64,71,70)(38,65,72,76)(45,52,73,75)(50,60,74,77)

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, 26969);