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C3×C5⋊(D89⋊C11) #44440336

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

Aliases

direct productC3×C5⋊(D89⋊C11)
unambiguous semidirect productC5⋊(C3×D89⋊C11)
unambiguous semidirect productD445⋊(C3×C11)
unambiguous semidirect product(C89⋊C11)⋊(C3×D5)
unambiguous semidirect product(C3×D445)⋊C11

Splittings

Fitting, socle, HallC3×C5×C89 ⋊ C2×C11
derived, HallC5×C89 ⋊ C2×C3×C11
HallC3×C5×C89⋊C11 ⋊ C2
HallC5×C89⋊C11 ⋊ C2×C3
HallC3×C89⋊C11 ⋊ D5
HallC3×D445 ⋊ C11
HallC89⋊C11 ⋊ C3×D5
HallD445 ⋊ C3×C11
HallC3×C89 ⋊ D5×C11
SylowC89 ⋊ C3×D5×C11
HallC3×C5 ⋊ D89⋊C11
SylowC5 ⋊ C3×D89⋊C11

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(D89⋊C11)
commutator, cosocle, hypocenterC5×C89C2×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C89C2×C11
LCSG ▷ C5×C89
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1335

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 21);