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C17×#63121⋊C3 #27210487

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

Aliases

direct productC17×#63121⋊C3
unambiguous semidirect product#63121⋊(C3×C17)
unambiguous semidirect product(C17×#63121)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C17
HallC17×#63121 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC17×C13⋊C3 ⋊ AGL(1,𝔽5)
Hall#63121 ⋊ C3×C17
HallC13×C17 ⋊ C3×AGL(1,𝔽5)
HallC5×C13⋊C3 ⋊ C4×C17
HallC5×C17 ⋊ AGL(1,𝔽13)
HallC13⋊C3 ⋊ C17×AGL(1,𝔽5)
SylowC13 ⋊ C3×C17×AGL(1,𝔽5)
SylowC5 ⋊ C17×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC17#63121⋊C3
commutator, hypocenterC5×C13C3×C4×C17
FrattiniC1G
Fitting, socleC5×C13×C17C3×C4
prime radicalC17×C5⋊(D13⋊C3)C2
cosocleD65C2×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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 37);