Finite Group Databasebeta

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D3×#16840847 #37552897

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

Aliases

direct productD3×#16840847
unambiguous semidirect productC3⋊(C2×#16840847)

Splittings

Fitting, socle, derived, HallC3×C11×C71 ⋊ C2×C5
HallC3×#16840847 ⋊ C2
HallD3×C11×C71 ⋊ C5
HallC11×C71 ⋊ C5×D3
HallD3×C71 ⋊ C11⋊C5
HallC3×C71 ⋊ C2×C11⋊C5
SylowC71 ⋊ D3×C11⋊C5
HallD3×C11 ⋊ C71⋊C5
HallC3×C11 ⋊ C2×C71⋊C5
SylowC11 ⋊ D3×C71⋊C5
SylowC3 ⋊ C2×#16840847

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 46);