Finite Group Databasebeta

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C3×C5×D89⋊C11 #44440334

order29370
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D89⋊C11
unambiguous semidirect productD89⋊(C3×C5×C11)
unambiguous semidirect product(C3×D89)⋊(C5×C11)
unambiguous semidirect product(C5×D89)⋊(C3×C11)
unambiguous semidirect product(C89⋊C11)⋊(C2×C3×C5)
unambiguous semidirect product(C3×C5×D89)⋊C11

Splittings

Fitting, socle, HallC3×C5×C89 ⋊ C2×C11
derived, SylowC89 ⋊ C2×C3×C5×C11
HallC3×C5×C89⋊C11 ⋊ C2
HallC5×C89⋊C11 ⋊ C2×C3
HallC3×C89⋊C11 ⋊ C2×C5
HallC3×C5×D89 ⋊ C11
HallC89⋊C11 ⋊ C2×C3×C5
HallC5×D89 ⋊ C3×C11
HallC3×D89 ⋊ C5×C11
HallC5×C89 ⋊ C2×C3×C11
HallC3×C89 ⋊ C2×C5×C11
HallD89 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5D89⋊C11
commutator, cosocle, hypocenterC89C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C89C2×C11
LCSG ▷ C89
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1335

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 19);