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D29×D165 #34062391

order19140
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD29×D165
unambiguous semidirect product(C3×D29)⋊D55
unambiguous semidirect product(C5×D29)⋊D33
unambiguous semidirect product(C11×D29)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C11×C29 ⋊ C22
HallC5×C11×C29 ⋊ C2×D3
HallC3×C11×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D11
HallC11×C29 ⋊ C2×D15
HallC3×C5×C11 ⋊ C2×D29
HallC5×C29 ⋊ C2×D33
HallC3×C29 ⋊ C2×D55
HallC5×C11 ⋊ D3×D29
HallC3×C11 ⋊ D5×D29
SylowC29 ⋊ C2×D165
HallC3×C5 ⋊ D11×D29
SylowC11 ⋊ D15×D29
SylowC5 ⋊ D29×D33
SylowC3 ⋊ D29×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C29C22
LCSG ▷ C3×C5×C11×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 84);