Finite Group Databasebeta

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C7×C11×D225 #46831373

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D225
unambiguous semidirect productC9⋊(C7×C11×D25)
unambiguous semidirect productC25⋊(C7×C11×D9)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC9×C25 ⋊ C2×C7×C11
HallC9×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ D9
HallC7×C9×C25 ⋊ C2×C11
HallC7×C9×C11 ⋊ D25
HallC11×C25 ⋊ C7×D9
HallC7×C25 ⋊ C11×D9
HallC9×C11 ⋊ C7×D25
HallC7×C9 ⋊ C11×D25
SylowC25 ⋊ C7×C11×D9
SylowC9 ⋊ C7×C11×D25

Subgroups

subgroupG/H
center, hypercenterC7×C11D225
commutator, cosocle, hypocenterC9×C25C2×C7×C11
FrattiniC3×C5C7×C11×D15
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11D15
LCSG ▷ C9×C25
UCSC1 ◁ C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 16);