Finite Group Databasebeta

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C89×D165 #44440332

order29370
automorphism?
homologyAbelianization (H1) = C2×C89 · Schur multiplier (H2) = C1

Aliases

direct productC89×D165
unambiguous semidirect productC3⋊(C89×D55)
unambiguous semidirect productC5⋊(D33×C89)
unambiguous semidirect productC11⋊(D15×C89)

Splittings

Fitting, socle, HallC3×C5×C11×C89 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C89
HallC5×C11×C89 ⋊ D3
HallC3×C11×C89 ⋊ D5
HallC3×C5×C89 ⋊ D11
HallC11×C89 ⋊ D15
HallC5×C89 ⋊ D33
HallC3×C89 ⋊ D55
HallC5×C11 ⋊ D3×C89
HallC3×C11 ⋊ D5×C89
HallC3×C5 ⋊ D11×C89
SylowC11 ⋊ D15×C89
SylowC5 ⋊ D33×C89
SylowC3 ⋊ C89×D55

Subgroups

subgroupG/H
center, hypercenterC89D165
commutator, cosocle, hypocenterC3×C5×C11C2×C89
FrattiniC1G
Fitting, socleC3×C5×C11×C89C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C89

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14685

Conjugacy classes & character table

7476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 17);