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AGL(1,𝔽13)×C29⋊C7 #44539770

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽13)×C29⋊C7
unambiguous semidirect product#261⋊(C3×C29⋊C7)
unambiguous semidirect product(C29×AGL(1,𝔽13))⋊C7
unambiguous semidirect product(#261×C29⋊C7)⋊C3

Splittings

Fitting, socle, derived, HallC13×C29 ⋊ C3×C4×C7
Hall#261×C29⋊C7 ⋊ C3
HallC13⋊C3×C29⋊C7 ⋊ C4
HallC29×AGL(1,𝔽13) ⋊ C7
HallC13×C29⋊C7 ⋊ C3×C4
HallC29×#261 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C4×C7
Hall#261 ⋊ C3×C29⋊C7
HallC13⋊C3 ⋊ C4×C29⋊C7
SylowC29 ⋊ C7×AGL(1,𝔽13)
SylowC13 ⋊ C3×C4×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C29C3×C4×C7
prime radicalD13⋊C3×C29⋊C7C2
cosocleD13×C29C2×C3×C7
LCSG ▷ C13×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 377

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 65);