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C3×C89×AGL(1,𝔽11) #44440342

order29370
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C89 · Schur multiplier (H2) = C1

Aliases

direct productC3×C89×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C89)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C89)
unambiguous semidirect product(C3×D11)⋊(C5×C89)
unambiguous semidirect product(D11×C89)⋊(C3×C5)
unambiguous semidirect product(C3×D11×C89)⋊C5

Splittings

Fitting, socle, HallC3×C11×C89 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C89
HallC3×C11⋊C5×C89 ⋊ C2
HallC3×D11×C89 ⋊ C5
HallC11⋊C5×C89 ⋊ C2×C3
HallD11×C89 ⋊ C3×C5
HallC11×C89 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C89
HallC3×D11 ⋊ C5×C89
HallC11⋊C5 ⋊ C2×C3×C89
HallC3×C11 ⋊ C2×C5×C89
HallD11 ⋊ C3×C5×C89

Subgroups

subgroupG/H
center, hypercenterC3×C89AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C89
FrattiniC1G
Fitting, socleC3×C11×C89C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C89

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2937

Conjugacy classes & character table

2937 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 27);