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C3×(C11⋊C5)⋊D89 #44440343

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

Aliases

direct productC3×(C11⋊C5)⋊D89
unambiguous semidirect product(C11⋊C5)⋊(C3×D89)
unambiguous semidirect productC89⋊(C3×AGL(1,𝔽11))
unambiguous semidirect productD979⋊(C3×C5)
unambiguous semidirect product(C3×D979)⋊C5

Splittings

Fitting, socle, HallC3×C11×C89 ⋊ C2×C5
derived, HallC11×C89 ⋊ C2×C3×C5
HallC3×C11⋊C5×C89 ⋊ C2
HallC3×D979 ⋊ C5
HallC11⋊C5×C89 ⋊ C2×C3
HallD979 ⋊ C3×C5
HallC3×C89 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D89
SylowC89 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D89
HallC3×C11 ⋊ C5×D89
SylowC11 ⋊ C3×C5×D89

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊D89
commutator, cosocle, hypocenterC11×C89C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C89C2×C5
LCSG ▷ C11×C89
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2937

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 28);