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C13×ΓL(1,𝔽8)×D33 #31825063

order18018
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×D33
unambiguous semidirect productC3⋊(C13×ΓL(1,𝔽8)×D11)
unambiguous semidirect productC11⋊(D3×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D33)⋊(C3×C13)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C2×C3
derivedC3×C7×C11 ⋊ C2×C3×C13
HallC3×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×C11×C13 ⋊ C3×D3
HallC3×C13×ΓL(1,𝔽8) ⋊ D11
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C13
HallC11×C13 ⋊ D3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×D33
HallC7×C11 ⋊ C3×D3×C13
HallC3×ΓL(1,𝔽8) ⋊ C13×D11
SylowC11 ⋊ D3×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×D33

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)×D33
commutator, cosocle, hypocenterC3×C7×C11C2×C3×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11
UCSC1 ◁ C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×AGL(1,𝔽7)×D33, D33×ΓL(1,𝔽8)⋊D13, C13×D33⋊AGL(1,𝔽7), …
maximal normal subgroup ofC13×AGL(1,𝔽7)×D33, D33×ΓL(1,𝔽8)⋊D13, C13×D33⋊AGL(1,𝔽7), …
maximal quotient ofC13×ΓL(1,𝔽8)×Dic33, C2×C13×ΓL(1,𝔽8)×D33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 108);