Finite Group Databasebeta

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C3×C11×D71⋊C5 #37552874

order23430
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D71⋊C5
unambiguous semidirect productD71⋊(C3×C5×C11)
unambiguous semidirect product(C71⋊C5)⋊(C2×C3×C11)
unambiguous semidirect product(C3×D71)⋊(C5×C11)

Splittings

Fitting, socle, HallC3×C11×C71 ⋊ C2×C5
derived, SylowC71 ⋊ C2×C3×C5×C11
HallC3×C11×C71⋊C5 ⋊ C2
HallC3×C11×D71 ⋊ C5
HallC11×C71⋊C5 ⋊ C2×C3
HallC11×D71 ⋊ C3×C5
HallC3×C71⋊C5 ⋊ C2×C11
HallC11×C71 ⋊ C2×C3×C5
HallC3×D71 ⋊ C5×C11
HallC71⋊C5 ⋊ C2×C3×C11
HallC3×C71 ⋊ C2×C5×C11
HallD71 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D71⋊C5
commutator, cosocle, hypocenterC71C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C71C2×C5
LCSG ▷ C71
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 23);