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C5×C17×AGL(1,𝔽13) #27210476

order13260
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C5×C17)
unambiguous semidirect product(C5×#261)⋊(C3×C17)
unambiguous semidirect product(C17×#261)⋊(C3×C5)
unambiguous semidirect product(C5×C17×#261)⋊C3

Splittings

Fitting, socle, HallC5×C13×C17 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C5×C17
HallC5×C17×#261 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC17×#261 ⋊ C3×C5
HallC17×C13⋊C3 ⋊ C4×C5
HallC5×#261 ⋊ C3×C17
HallC13×C17 ⋊ C3×C4×C5
HallC5×C13⋊C3 ⋊ C4×C17
HallC5×C13 ⋊ C3×C4×C17
Hall#261 ⋊ C3×C5×C17
HallC13⋊C3 ⋊ C4×C5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C5×C17
FrattiniC1G
Fitting, socleC5×C13×C17C3×C4
prime radicalC5×C17×D13⋊C3C2
cosocleD13C2×C3×C5×C17
LCSG ▷ C13
UCSC1 ◁ C5×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:

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

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 26);