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C2×C3⋊(C5⋊AGL(1,𝔽23)) #29503265

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

Aliases

direct productC2×C3⋊(C5⋊AGL(1,𝔽23))
unambiguous semidirect product(C2×C3)⋊(C5⋊AGL(1,𝔽23))
unambiguous semidirect product(C2×C5)⋊(C3⋊AGL(1,𝔽23))
unambiguous semidirect product(C2×C23⋊C11)⋊D15
unambiguous semidirect product(C2×D345)⋊C11

Splittings

Fitting, socleC2×C3×C5×C23 ⋊ C2×C11
derived, HallC3×C5×C23 ⋊ C22×C11
HallC3×C5×C23⋊C11 ⋊ C22
HallC2×D345 ⋊ 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 ⋊ C2×C3⋊AGL(1,𝔽23)
SylowC3 ⋊ C2×C5⋊AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊AGL(1,𝔽23))
commutator, cosocle, hypocenterC3×C5×C23C22×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C23C2×C11
LCSG ▷ C3×C5×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 51);