Finite Group Databasebeta

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C3⋊((C71⋊C5)⋊D11) #37552910

order23430
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C71⋊C5)⋊D11)
unambiguous semidirect product(C71⋊C5)⋊D33

Splittings

Fitting, socle, derived, HallC3×C11×C71 ⋊ C2×C5
HallC3×C11×C71⋊C5 ⋊ C2
HallD2343 ⋊ C5
HallC11×C71⋊C5 ⋊ D3
HallC3×C71⋊C5 ⋊ D11
HallC11×C71 ⋊ C5×D3
HallC71⋊C5 ⋊ D33
HallC3×C71 ⋊ C5×D11
SylowC71 ⋊ C5×D33
HallC3×C11 ⋊ D71⋊C5
SylowC11 ⋊ C3⋊(D71⋊C5)
SylowC3 ⋊ (C71⋊C5)⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C71C2×C5
LCSG ▷ C3×C11×C71
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Polycyclic presentation:

2,3,5,11,71|b^a=b^2,d^a=d^10,e^a=e^70,e^c=e^54

Conjugacy classes & character table

321 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 59);