Finite Group Databasebeta

← Prev (#44440336) Next (#44440338) →

C5×D3×C89⋊C11 #44440337

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

Aliases

direct productC5×D3×C89⋊C11
unambiguous semidirect productC3⋊(C2×C5×C89⋊C11)
unambiguous semidirect product(D3×C89)⋊(C5×C11)
unambiguous semidirect product(C5×D3×C89)⋊C11

Splittings

Fitting, socle, HallC3×C5×C89 ⋊ C2×C11
derived, HallC3×C89 ⋊ C2×C5×C11
HallC3×C5×C89⋊C11 ⋊ C2
HallC3×C89⋊C11 ⋊ C2×C5
HallC5×D3×C89 ⋊ C11
HallD3×C89 ⋊ C5×C11
HallC5×C89 ⋊ D3×C11
SylowC89 ⋊ C5×D3×C11
HallC3×C5 ⋊ C2×C89⋊C11
SylowC3 ⋊ C2×C5×C89⋊C11

Subgroups

subgroupG/H
center, hypercenterC5D3×C89⋊C11
commutator, cosocle, hypocenterC3×C89C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C89C2×C11
LCSG ▷ C3×C89
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1335

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 22);