Finite Group Databasebeta

← Prev (#72295331) Next (#72295333) →

C2×D14993 #72295332

order59972
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD29986
direct productC2×D14993

Splittings

Fitting, socleC2×C11×C29×C47 ⋊ C2
derived, HallC11×C29×C47 ⋊ C22
HallC29×C47 ⋊ C2×D11
HallC11×C47 ⋊ C2×D29
HallC11×C29 ⋊ C2×D47
SylowC47 ⋊ C2×D319
SylowC29 ⋊ C2×D517
SylowC11 ⋊ C2×D1363

Subgroups

subgroupG/H
center, hypercenterC2D14993
commutator, cosocle, hypocenterC11×C29×C47C22
FrattiniC1G
Fitting, socleC2×C11×C29×C47C2
LCSG ▷ C11×C29×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 89
transitive degreeμt(G) = 29986

A minimal faithful permutation representation — 2 generators on 89 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(4,13)(5,12)(6,11)(7,10)(8,9)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)

Conjugacy classes & character table

14996 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89), (4,13)(5,12)(6,11)(7,10)(8,9)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67));