Finite Group Databasebeta

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D3×D23×C11⋊C5 #29503273

order15180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×D23×C11⋊C5
unambiguous semidirect product(D3×C23)⋊(C2×C11⋊C5)
unambiguous semidirect product(C3×D23)⋊(C2×C11⋊C5)
unambiguous semidirect productD69⋊(C2×C11⋊C5)
unambiguous semidirect product(D3×C11×D23)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C23 ⋊ C22×C5
HallC3×C23×C11⋊C5 ⋊ C22
HallD3×C11×D23 ⋊ C5
HallC23×C11⋊C5 ⋊ C2×D3
HallC11×C23 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D23
HallC3×C23 ⋊ C22×C11⋊C5
HallC3×C11 ⋊ C2×C5×D23
SylowC23 ⋊ C2×D3×C11⋊C5
SylowC11 ⋊ C5×D3×D23
SylowC3 ⋊ C2×D23×C11⋊C5

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 759

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 59);