Finite Group Databasebeta

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C9×D1925 #46831368

order34650
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D1925
unambiguous semidirect productC11⋊(C9×D175)
unambiguous semidirect productC25⋊(C9×D77)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC7×C11×C25 ⋊ C2×C9
HallC9×C11×C25 ⋊ D7
HallC7×C9×C25 ⋊ D11
HallC7×C9×C11 ⋊ D25
HallC11×C25 ⋊ C9×D7
HallC9×C25 ⋊ D77
HallC7×C25 ⋊ C9×D11
HallC9×C11 ⋊ D175
HallC7×C11 ⋊ C9×D25
HallC7×C9 ⋊ D275
SylowC25 ⋊ C9×D77
SylowC11 ⋊ C9×D175
SylowC7 ⋊ C9×D275

Subgroups

subgroupG/H
center, hypercenterC9D1925
commutator, hypocenterC7×C11×C25C2×C9
FrattiniC3×C5C3×D385
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C3×D5
prime radicalC3×D1925C3
cosocleC3×C7×C11×C25C2×C3
LCSG ▷ C7×C11×C25
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 11);