Finite Group Databasebeta

← Prev (#32912508) Next (#32912510) →

C3×C5×ΓL(1,𝔽8)⋊D29 #32912509

order18270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)⋊D29
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C5×D29)
unambiguous semidirect productC29⋊(C3×C5×AGL(1,𝔽7))
unambiguous semidirect productD203⋊(C32×C5)
unambiguous semidirect product(C3×D203)⋊(C3×C5)
unambiguous semidirect product(C5×D203)⋊C32
unambiguous semidirect product(C3×C5×D203)⋊C3

Splittings

Fitting, socleC3×C5×C7×C29 ⋊ C2×C3
derived, HallC7×C29 ⋊ C2×C32×C5
HallC3×C5×ΓL(1,𝔽8)×C29 ⋊ C2
HallC5×D203 ⋊ C32
HallC3×ΓL(1,𝔽8)×C29 ⋊ C2×C5
HallC5×C7×C29 ⋊ C2×C32
HallD203 ⋊ C32×C5
HallC3×C5×ΓL(1,𝔽8) ⋊ D29
HallC5×C29 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C5×D29
HallC5×C7 ⋊ C32×D29
SylowC29 ⋊ C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C32×C5×D29

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D29
commutator, cosocle, hypocenterC7×C29C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C29C2×C3
LCSG ▷ C7×C29
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×AGL(1,𝔽7)×D29, C3×D5×ΓL(1,𝔽8)⋊D29, C3×(C5⋊AGL(1,𝔽7))⋊D29, …
maximal normal subgroup ofC3×C5×AGL(1,𝔽7)×D29, C3×D5×ΓL(1,𝔽8)⋊D29, C3×(C5⋊AGL(1,𝔽7))⋊D29, …
maximal quotient ofC3×C5×ΓL(1,𝔽8)⋊Dic29, C2×C3×C5×ΓL(1,𝔽8)⋊D29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 47);