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C5×C3⋊(D89⋊C11) #44440338

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

Aliases

direct productC5×C3⋊(D89⋊C11)
unambiguous semidirect productC3⋊(C5×D89⋊C11)
unambiguous semidirect productD267⋊(C5×C11)
unambiguous semidirect product(C89⋊C11)⋊(C5×D3)
unambiguous semidirect product(C5×D267)⋊C11

Splittings

Fitting, socle, HallC3×C5×C89 ⋊ C2×C11
derived, HallC3×C89 ⋊ C2×C5×C11
HallC3×C5×C89⋊C11 ⋊ C2
HallC5×C89⋊C11 ⋊ D3
HallC3×C89⋊C11 ⋊ C2×C5
HallC5×D267 ⋊ C11
HallC89⋊C11 ⋊ C5×D3
HallD267 ⋊ C5×C11
HallC5×C89 ⋊ D3×C11
SylowC89 ⋊ C5×D3×C11
HallC3×C5 ⋊ D89⋊C11
SylowC3 ⋊ C5×D89⋊C11

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D89⋊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

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 23);