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C5×C13⋊C3×#595 #27210482

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

Aliases

direct productC5×C13⋊C3×#595
unambiguous semidirect product(C13×#595)⋊(C3×C5)
unambiguous semidirect product(C5×C13×#595)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×#595
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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 32);