Finite Group Databasebeta

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C7×C29×AGL(1,𝔽13) #44539806

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC7×C29×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C7×C29)

Splittings

Fitting, socle, HallC7×C13×C29 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C7×C29
HallC7×C29×#261 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C4
HallC29×#261 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C4×C7
HallC13×C29 ⋊ C3×C4×C7
HallC7×#261 ⋊ C3×C29
HallC7×C13⋊C3 ⋊ C4×C29
HallC7×C13 ⋊ C3×C4×C29
Hall#261 ⋊ C3×C7×C29
HallC13⋊C3 ⋊ C4×C7×C29

Subgroups

subgroupG/H
center, hypercenterC7×C29AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C7×C29
FrattiniC1G
Fitting, socleC7×C13×C29C3×C4
prime radicalC7×C29×D13⋊C3C2
cosocleD13C2×C3×C7×C29
LCSG ▷ C13
UCSC1 ◁ C7×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

2639 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 101);