Finite Group Databasebeta

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C3⋊((C11⋊C5)⋊D71) #37552911

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

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊D71)
unambiguous semidirect product(C11⋊C5)⋊D213

Splittings

Fitting, socle, derived, HallC3×C11×C71 ⋊ C2×C5
HallC3×C11⋊C5×C71 ⋊ C2
HallD2343 ⋊ C5
HallC11⋊C5×C71 ⋊ D3
HallC11×C71 ⋊ C5×D3
HallC3×C71 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D71
SylowC71 ⋊ C3⋊AGL(1,𝔽11)
HallC11⋊C5 ⋊ D213
HallC3×C11 ⋊ C5×D71
SylowC11 ⋊ C5×D213
SylowC3 ⋊ (C11⋊C5)⋊D71

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,d^c=d^4

Conjugacy classes & character table

753 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 60);