Finite Group Databasebeta

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C5×C7×D9×C11⋊C5 #46831471

order34650
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×D9×C11⋊C5
unambiguous semidirect productC9⋊(C2×C5×C7×C11⋊C5)
unambiguous semidirect product(C11×D9)⋊(C52×C7)
unambiguous semidirect product(C5×C11×D9)⋊(C5×C7)
unambiguous semidirect product(C7×C11×D9)⋊C52
unambiguous semidirect product(C5×C7×C11×D9)⋊C5

Splittings

FittingC5×C7×C9×C11 ⋊ C2×C5
derived, HallC9×C11 ⋊ C2×C52×C7
HallC5×C7×C9×C11⋊C5 ⋊ C2
HallC5×C9×C11⋊C5 ⋊ C2×C7
HallC7×C11×D9 ⋊ C52
HallC7×C9×C11 ⋊ C2×C52
HallC11×D9 ⋊ C52×C7
HallC7×C11 ⋊ C52×D9
HallC7×C9 ⋊ C2×C5×C11⋊C5
SylowC11 ⋊ C52×C7×D9
SylowC9 ⋊ C2×C5×C7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5×C7D9×C11⋊C5
commutator, cosocle, hypocenterC9×C11C2×C52×C7
FrattiniC3C5×D3×C7×C11⋊C5
FittingC5×C7×C9×C11C2×C5
socleC3×C5×C7×C11C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C5×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 114);