Finite Group Databasebeta

← Prev (#26046204) Next (#26046206) →

C19×ΓL(1,𝔽8)×D15 #26046205

order11970
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×ΓL(1,𝔽8)×D15
unambiguous semidirect productC3⋊(D5×C19×ΓL(1,𝔽8))
unambiguous semidirect productC5⋊(D3×C19×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D15)⋊(C3×C19)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derivedC3×C5×C7 ⋊ C2×C3×C19
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C2
HallC3×C19×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×C19 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C19
HallC7×C19 ⋊ C3×D15
HallC5×C19 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D5×C19
HallC5×C7 ⋊ C3×D3×C19
SylowC7 ⋊ C3×C19×D15
SylowC5 ⋊ D3×C19×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)×D15
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C19
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C19

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×D15×AGL(1,𝔽7), D15×ΓL(1,𝔽8)⋊D19, ΓL(1,𝔽8)×D15×D19, …
maximal normal subgroup ofC19×D15×AGL(1,𝔽7), D15×ΓL(1,𝔽8)⋊D19, ΓL(1,𝔽8)×D15×D19, …
maximal quotient ofC19×ΓL(1,𝔽8)×Dic15, C2×C19×ΓL(1,𝔽8)×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 134);