Finite Group Databasebeta

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C9×C11×D175 #46831367

order34650
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D175
unambiguous semidirect productC25⋊(C9×C11×D7)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC7×C25 ⋊ C2×C9×C11
HallC9×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ C2×C9
HallC7×C9×C25 ⋊ C2×C11
HallC7×C9×C11 ⋊ D25
HallC11×C25 ⋊ C9×D7
HallC9×C25 ⋊ C11×D7
HallC7×C11 ⋊ C9×D25
HallC7×C9 ⋊ C11×D25
SylowC25 ⋊ C9×C11×D7
SylowC7 ⋊ C9×C11×D25

Subgroups

subgroupG/H
center, hypercenterC9×C11D175
commutator, hypocenterC7×C25C2×C9×C11
FrattiniC3×C5C3×C11×D35
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C3×D5
prime radicalC3×C11×D175C3
cosocleC3×C7×C25C2×C3×C11
LCSG ▷ C7×C25
UCSC1 ◁ C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8811 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 10);