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C2×(C11⋊C5)⋊(D43⋊C3) #43248792

order28380
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C11⋊C5)⋊(D43⋊C3)
unambiguous semidirect product(C2×C11⋊C5)⋊(D43⋊C3)
unambiguous semidirect product(C2×C43⋊C3)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊(D43⋊C3))⋊C5
unambiguous semidirect product(C2×C43⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC2×C11×C43 ⋊ C2×C3×C5
derived, HallC11×C43 ⋊ C22×C3×C5
HallC2×C43⋊AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×C43⋊C3 ⋊ C22
HallC2×C11⋊(D43⋊C3) ⋊ C5
HallC43×C11⋊C5 ⋊ C22×C3
HallC2×D473 ⋊ C3×C5
HallC11×C43⋊C3 ⋊ C22×C5
HallC43⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D43⋊C3
SylowC43 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2(C11⋊C5)⋊(D43⋊C3)
commutator, cosocle, hypocenterC11×C43C22×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C43C2×C3×C5
LCSG ▷ C11×C43
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 946

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 39);