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D15×AGL(1,𝔽23) #29503254

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

Aliases

direct productD15×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C11×D15)
unambiguous semidirect product(D15×D23)⋊C11
unambiguous semidirect product(C3×AGL(1,𝔽23))⋊D5
unambiguous semidirect product(C5×AGL(1,𝔽23))⋊D3

Splittings

Fitting, socle, derived, HallC3×C5×C23 ⋊ C22×C11
HallC3×C5×C23⋊C11 ⋊ C22
HallD15×D23 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×D3
HallC3×C23⋊C11 ⋊ C2×D5
HallC23⋊C11 ⋊ C2×D15
HallC5×C23 ⋊ C2×D3×C11
HallC3×C23 ⋊ C2×D5×C11
SylowC23 ⋊ C2×C11×D15
HallC3×C5 ⋊ C2×AGL(1,𝔽23)
SylowC5 ⋊ D3×AGL(1,𝔽23)
SylowC3 ⋊ D5×AGL(1,𝔽23)

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

207 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 40);