Finite Group Databasebeta

← Prev (#49136182) Next (#49136184) →

C2×D9061 #49136183

order36244
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18122
direct productC2×D9061
unambiguous semidirect product(C2×C13)⋊D697
unambiguous semidirect product(C2×C17)⋊D533
unambiguous semidirect product(C2×C41)⋊D221

Splittings

Fitting, socleC2×C13×C17×C41 ⋊ C2
derived, HallC13×C17×C41 ⋊ C22
HallC17×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×D17
HallC13×C17 ⋊ C2×D41
SylowC41 ⋊ C2×D221
SylowC17 ⋊ C2×D533
SylowC13 ⋊ C2×D697

Subgroups

subgroupG/H
center, hypercenterC2D9061
commutator, cosocle, hypocenterC13×C17×C41C22
FrattiniC1G
Fitting, socleC2×C13×C17×C41C2
LCSG ▷ C13×C17×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 18122

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

Conjugacy classes & character table

9064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36244, 51);