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C3⋊(C11⋊((C13⋊C3)⋊D7)) #31825071

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

Aliases

unambiguous semidirect productC3⋊(C11⋊((C13⋊C3)⋊D7))
unambiguous semidirect productC11⋊(C3⋊((C13⋊C3)⋊D7))
unambiguous semidirect product(C13⋊C3)⋊D231

Splittings

Fitting, socle, derivedC3×C7×C11×C13 ⋊ C2×C3
HallC3×C7×C11×C13⋊C3 ⋊ C2
HallC3×C11×C13⋊C3 ⋊ D7
HallC7×C11×C13 ⋊ C3×D3
HallC3×C7×C13⋊C3 ⋊ D11
HallC11×C13 ⋊ C3×D21
HallC3×C13⋊C3 ⋊ D77
HallC7×C13 ⋊ C3×D33
HallC7×C11 ⋊ C3⋊(D13⋊C3)
SylowC13 ⋊ C3×D231
SylowC11 ⋊ C3⋊((C13⋊C3)⋊D7)
SylowC7 ⋊ C3⋊(C11⋊(D13⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Polycyclic presentation:

2,3^2,7,11,13|c^a=c^2,d^a=d^6,e^a=e^10,f^a=f^12,f^b=f^3

Conjugacy classes & character table

813 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×D231, D11×C3⋊((C13⋊C3)⋊D7), D21×C11⋊(D13⋊C3), …
maximal normal subgroup ofD13⋊C3×D231, D11×C3⋊((C13⋊C3)⋊D7), D21×C11⋊(D13⋊C3), …
maximal quotient ofC3⋊(C11⋊#11763955), C2×C3⋊(C11⋊((C13⋊C3)⋊D7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 116);