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C17×#63118⋊C3 #27210499

order13260
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×#63118⋊C3
unambiguous semidirect product#63118⋊(C3×C17)
unambiguous semidirect product(C17×#63118)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C17
HallC17×#63118 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC17×C13⋊C3 ⋊ Dic5
Hall#63118 ⋊ C3×C17
HallC13×C17 ⋊ C3×Dic5
HallC5×C13⋊C3 ⋊ C4×C17
HallC5×C17 ⋊ AGL(1,𝔽13)
HallC13⋊C3 ⋊ C17×Dic5
SylowC13 ⋊ C3×C17×Dic5
SylowC5 ⋊ C17×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC17#63118⋊C3
commutator, hypocenterC5×C13C3×C4×C17
FrattiniC1G
Fitting, socleC5×C13×C17C3×C4
prime radicalC5×C17×D13⋊C3C2
cosocleC5×D13C2×C3×C17
LCSG ▷ C5×C13
UCSC1 ◁ C17

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 49);