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C5×#11725131⋊C3 #27210478

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

Aliases

direct productC5×#11725131⋊C3
unambiguous semidirect product#11725131⋊(C3×C5)
unambiguous semidirect product(C5×#11725131)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C3×C4
derived, HallC13×C17 ⋊ C3×C4×C5
HallC5×#11725131 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
Hall#11725131 ⋊ C3×C5
HallC17×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ #595
HallC5×C17 ⋊ AGL(1,𝔽13)
HallC5×C13 ⋊ C3×#595
HallC13⋊C3 ⋊ C5×#595
SylowC17 ⋊ C5×AGL(1,𝔽13)
SylowC13 ⋊ C3×C5×#595

Subgroups

subgroupG/H
center, hypercenterC5#11725131⋊C3
commutator, hypocenterC13×C17C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C17C3×C4
prime radicalC5×C17⋊(D13⋊C3)C2
cosocleD221C2×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)(5,8,9,14)(7,10,12,11)(13,15,16,17)(19,23,28,24,21,25,22,29,26,20,27,30)(31,32,33,34,35);(1,2,5,10,3,7,13,15,8,14,17,16,12,6,11,9,4)(18,19,23,21,28,20,25,30,24,26,27,29,22)

Conjugacy classes & character table

205 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 28);