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D3×D5×C23⋊C11 #29503258

order15180
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×D5×C23⋊C11
unambiguous semidirect product(C5×D3)⋊(C2×C23⋊C11)
unambiguous semidirect product(C3×D5)⋊(C2×C23⋊C11)
unambiguous semidirect productD15⋊(C2×C23⋊C11)
unambiguous semidirect product(D3×D5×C23)⋊C11

Splittings

Fitting, socle, derived, HallC3×C5×C23 ⋊ C22×C11
HallC3×C5×C23⋊C11 ⋊ C22
HallD3×D5×C23 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×D3
HallC3×C23⋊C11 ⋊ C2×D5
HallC5×C23 ⋊ C2×D3×C11
HallC3×C23 ⋊ C2×D5×C11
SylowC23 ⋊ D3×D5×C11
HallC3×C5 ⋊ C22×C23⋊C11
SylowC5 ⋊ C2×D3×C23⋊C11
SylowC3 ⋊ C2×D5×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C23C22×C11
LCSG ▷ C3×C5×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 345

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 44);