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C2×D15283 #72295857

order61132
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD30566
direct productC2×D15283

Splittings

Fitting, socleC2×C17×C29×C31 ⋊ C2
derived, HallC17×C29×C31 ⋊ C22
HallC29×C31 ⋊ C2×D17
HallC17×C31 ⋊ C2×D29
HallC17×C29 ⋊ C2×D31
SylowC31 ⋊ C2×D493
SylowC29 ⋊ C2×D527
SylowC17 ⋊ C2×D899

Subgroups

subgroupG/H
center, hypercenterC2D15283
commutator, cosocle, hypocenterC17×C29×C31C22
FrattiniC1G
Fitting, socleC2×C17×C29×C31C2
LCSG ▷ C17×C29×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 30566

A minimal faithful permutation representation — 2 generators on 79 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);(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

15286 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), (4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65));