Finite Group Databasebeta

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C7×C11×D9×C25 #46831369

order34650
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D9×C25
unambiguous semidirect productC9⋊(C2×C7×C11×C25)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, SylowC9 ⋊ C2×C7×C11×C25
HallC9×C11×C25 ⋊ C2×C7
HallC7×C9×C25 ⋊ C2×C11
HallC7×C9×C11 ⋊ C2×C25
HallC9×C25 ⋊ C2×C7×C11
HallC9×C11 ⋊ C2×C7×C25
HallC7×C9 ⋊ C2×C11×C25

Subgroups

subgroupG/H
center, hypercenterC7×C11×C25D9
commutator, hypocenterC9C2×C7×C11×C25
FrattiniC3×C5C5×D3×C7×C11
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C5×D3
prime radicalC5×C7×C11×D9C5
cosocleC5×C9C2×C5×C7×C11
LCSG ▷ C9
UCSC1 ◁ C7×C11×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

11550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 12);