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C2×C3×C23⋊AGL(1,𝔽11) #29503277

order15180
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C23⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C23)⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D23)
unambiguous semidirect product(C2×D253)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D253)⋊C5

Splittings

Fitting, socleC2×C3×C11×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C22×C3×C5
HallC3×C23×C11⋊C5 ⋊ C22
HallC2×C3×D253 ⋊ C5
HallC23×C11⋊C5 ⋊ C22×C3
HallC2×D253 ⋊ C3×C5
HallC3×C11×C23 ⋊ C22×C5
HallC3×C11⋊C5 ⋊ C2×D23
HallC3×C23 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C3×D23
HallC3×C11 ⋊ C2×C5×D23
SylowC23 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C23C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1518

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 63);