Finite Group Databasebeta

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C7×C9×D275 #46831366

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×D275
unambiguous semidirect productC11⋊(C7×C9×D25)
unambiguous semidirect productC25⋊(C7×C9×D11)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC11×C25 ⋊ C2×C7×C9
HallC9×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C2×C9
HallC7×C9×C25 ⋊ D11
HallC7×C9×C11 ⋊ D25
HallC9×C25 ⋊ C7×D11
HallC7×C25 ⋊ C9×D11
HallC9×C11 ⋊ C7×D25
HallC7×C11 ⋊ C9×D25
SylowC25 ⋊ C7×C9×D11
SylowC11 ⋊ C7×C9×D25

Subgroups

subgroupG/H
center, hypercenterC7×C9D275
commutator, hypocenterC11×C25C2×C7×C9
FrattiniC3×C5C3×C7×D55
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C3×D5
prime radicalC3×C7×D275C3
cosocleC3×C11×C25C2×C3×C7
LCSG ▷ C11×C25
UCSC1 ◁ C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8757 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 9);