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D3×D1045 #27160085

order12540
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D1045
unambiguous semidirect product(C5×D3)⋊D209
unambiguous semidirect product(D3×C11)⋊D95
unambiguous semidirect product(D3×C19)⋊D55

Splittings

Fitting, socle, derived, HallC3×C5×C11×C19 ⋊ C22
HallC5×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D11
HallC11×C19 ⋊ D3×D5
HallC3×C5×C11 ⋊ C2×D19
HallC5×C19 ⋊ D3×D11
HallC3×C19 ⋊ C2×D55
HallC5×C11 ⋊ D3×D19
HallC3×C11 ⋊ C2×D95
SylowC19 ⋊ D3×D55
HallC3×C5 ⋊ C2×D209
SylowC11 ⋊ D3×D95
SylowC5 ⋊ D3×D209
SylowC3 ⋊ C2×D1045

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C19C22
LCSG ▷ C3×C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1572 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD9×D1045, D3×C5⋊(C11⋊(D19⋊C3)), C3×D3×D1045, …
maximal normal subgroup ofD3×C5⋊(C11⋊(D19⋊C3)), C3×D3×D1045
maximal quotient ofD9×D1045, C3×D3×D1045, D3×D3135, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 115);