Finite Group Databasebeta

← Prev (#27190252) Next (#27190254) →

C2×D5×#10620323 #27190253

order13140
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×#10620323
unambiguous semidirect productC5⋊(C22×#10620323)
unambiguous semidirect product(C2×C5)⋊(C2×#10620323)

Splittings

Fitting, socleC2×C5×C73 ⋊ C2×C9
derived, HallC5×C73 ⋊ C22×C9
HallC5×#10620323 ⋊ C22
HallC2×D5×C73 ⋊ C9
SylowC73 ⋊ C2×C9×D5
SylowC5 ⋊ C22×#10620323

Subgroups

subgroupG/H
center, hypercenterC2D5×#10620323
commutator, hypocenterC5×C73C22×C9
FrattiniC1G
Fitting, socleC2×C5×C73C2×C9
prime radicalC2×D5×C73⋊C3C3
cosocleC5×C73⋊C3C22×C3
LCSG ▷ C5×C73
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 80
transitive degreeμt(G) = 730

A minimal faithful permutation representation — 2 generators on 80 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13140, 87);