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C3×C11⋊C5×D89 #44440341

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

Aliases

direct productC3×C11⋊C5×D89
unambiguous semidirect productC89⋊(C2×C3×C11⋊C5)
unambiguous semidirect product(C11×D89)⋊(C3×C5)
unambiguous semidirect product(C3×C11×D89)⋊C5

Splittings

Fitting, socle, HallC3×C11×C89 ⋊ C2×C5
derived, HallC11×C89 ⋊ C2×C3×C5
HallC3×C11⋊C5×C89 ⋊ C2
HallC3×C11×D89 ⋊ C5
HallC11⋊C5×C89 ⋊ C2×C3
HallC11×D89 ⋊ C3×C5
HallC3×C89 ⋊ C2×C11⋊C5
SylowC89 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ C5×D89
SylowC11 ⋊ C3×C5×D89

Subgroups

subgroupG/H
center, hypercenterC3C11⋊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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 26);