Finite Group Databasebeta

← Prev (#31825061) Next (#31825063) →

C11×ΓL(1,𝔽8)×D39 #31825062

order18018
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×D39
unambiguous semidirect productC3⋊(C11×ΓL(1,𝔽8)×D13)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C2×C3
derivedC3×C7×C13 ⋊ C2×C3×C11
HallC3×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×C11×C13 ⋊ C3×D3
HallC3×C13×ΓL(1,𝔽8) ⋊ C2×C11
HallC3×C11×ΓL(1,𝔽8) ⋊ D13
HallC11×C13 ⋊ D3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×D3×C11
HallC7×C11 ⋊ C3×D39
HallC3×ΓL(1,𝔽8) ⋊ C11×D13
SylowC13 ⋊ D3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×D39

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×D39
commutator, cosocle, hypocenterC3×C7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×D39, C11×(C3⋊AGL(1,𝔽7))⋊D13, D39×C11⋊AGL(1,𝔽7), …
maximal normal subgroup ofC11×AGL(1,𝔽7)×D39, C11×(C3⋊AGL(1,𝔽7))⋊D13, D39×C11⋊AGL(1,𝔽7), …
maximal quotient ofC11×ΓL(1,𝔽8)×Dic39, C2×C11×ΓL(1,𝔽8)×D39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 107);