Finite Group Databasebeta

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D15×C89⋊C11 #44440339

order29370
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productD15×C89⋊C11
unambiguous semidirect productC3⋊(D5×C89⋊C11)
unambiguous semidirect productC5⋊(D3×C89⋊C11)
unambiguous semidirect product(D15×C89)⋊C11

Splittings

Fitting, socle, derived, HallC3×C5×C89 ⋊ C2×C11
HallC3×C5×C89⋊C11 ⋊ C2
HallC5×C89⋊C11 ⋊ D3
HallC3×C89⋊C11 ⋊ D5
HallD15×C89 ⋊ C11
HallC5×C89 ⋊ D3×C11
HallC3×C89 ⋊ D5×C11
SylowC89 ⋊ C11×D15
HallC3×C5 ⋊ C2×C89⋊C11
SylowC5 ⋊ D3×C89⋊C11
SylowC3 ⋊ D5×C89⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C89C2×C11
LCSG ▷ C3×C5×C89
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1335

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 24);