Finite Group Databasebeta

← Prev (#49180001) Next (#49180003) →

C31×ΓL(1,𝔽8)⋊D29 #49180002

order37758
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×ΓL(1,𝔽8)⋊D29
unambiguous semidirect productΓL(1,𝔽8)⋊(C31×D29)
unambiguous semidirect productC29⋊(C31×AGL(1,𝔽7))
unambiguous semidirect productD203⋊(C3×C31)

Splittings

Fitting, socle, HallC7×C29×C31 ⋊ C2×C3
derived, HallC7×C29 ⋊ C2×C3×C31
HallΓL(1,𝔽8)×C29×C31 ⋊ C2
HallC31×D203 ⋊ C3
HallC29×C31 ⋊ AGL(1,𝔽7)
HallΓL(1,𝔽8)×C31 ⋊ D29
HallΓL(1,𝔽8)×C29 ⋊ C2×C31
HallD203 ⋊ C3×C31
HallC7×C31 ⋊ C3×D29
SylowC29 ⋊ C31×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C31×D29
SylowC7 ⋊ C3×C31×D29

Subgroups

subgroupG/H
center, hypercenterC31ΓL(1,𝔽8)⋊D29
commutator, cosocle, hypocenterC7×C29C2×C3×C31
FrattiniC1G
Fitting, socleC7×C29×C31C2×C3
LCSG ▷ C7×C29
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6293

Conjugacy classes & character table

2387 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37758, 51);