Finite Group Databasebeta

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C29×AGL(1,𝔽31) #41004215

order26970
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C5×C29)
unambiguous semidirect product(D31⋊C5)⋊(C3×C29)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C2×C29)
unambiguous semidirect product(C29×D31⋊C3)⋊C5
unambiguous semidirect product(C29×D31⋊C5)⋊C3

Splittings

Fitting, socle, HallC29×C31 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C2×C3×C5×C29
HallC29×(C31⋊C3)⋊C5 ⋊ C2
HallC29×D31⋊C5 ⋊ C3
HallC29×D31⋊C3 ⋊ C5
HallC29×ΓL(1,𝔽32) ⋊ C2×C3
HallC29×C31⋊C3 ⋊ C2×C5
HallC29×D31 ⋊ C3×C5
Hall(C31⋊C3)⋊C5 ⋊ C2×C29
HallD31⋊C5 ⋊ C3×C29
HallD31⋊C3 ⋊ C5×C29
HallΓL(1,𝔽32) ⋊ C2×C3×C29
HallC31⋊C3 ⋊ C2×C5×C29
HallD31 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC29AGL(1,𝔽31)
commutator, cosocle, hypocenterC31C2×C3×C5×C29
FrattiniC1G
Fitting, socleC29×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 899

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 34);