Finite Group Databasebeta

← Prev (#27210479) Next (#27210481) →

C5×#11725133⋊C3 #27210480

order13260
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#11725133⋊C3
unambiguous semidirect product#11725133⋊(C3×C5)
unambiguous semidirect product(C5×#11725133)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C3×C4
derived, HallC13×C17 ⋊ C3×C4×C5
HallC5×#11725133 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
Hall#11725133 ⋊ C3×C5
HallC17×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ #595
HallC5×C17 ⋊ Dic13⋊C3
HallC5×C13 ⋊ C3×#595
HallC13⋊C3 ⋊ C5×#595
SylowC17 ⋊ C5×Dic13⋊C3
SylowC13 ⋊ C3×C5×#595

Subgroups

subgroupG/H
center, hypercenterC5#11725133⋊C3
commutator, hypocenterC13×C17C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C17C3×C4
prime radicalC5×D17×C13⋊C3C2
cosocleC13×D17C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1105

A minimal faithful permutation representation — 2 generators on 35 points:

(2,3,4,6)(5,8,9,13)(7,12,10,11)(14,16,17,15)(19,23,24,20,21,25)(22,29,28,26,27,30)(31,32,33,34,35);(1,2,5,10,6,11,15,17,13,8,14,16,12,3,7,9,4)(18,19,22,21,25,28,27,29,30,24,23,26,20)

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 30);