Finite Group Databasebeta

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C9×D1309 #37555615

order23562
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D1309
unambiguous semidirect productC11⋊(C9×D119)
unambiguous semidirect productC17⋊(C9×D77)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC7×C11×C17 ⋊ C2×C9
HallC9×C11×C17 ⋊ D7
HallC7×C9×C17 ⋊ D11
HallC7×C9×C11 ⋊ D17
HallC11×C17 ⋊ C9×D7
HallC9×C17 ⋊ D77
HallC7×C17 ⋊ C9×D11
HallC9×C11 ⋊ D119
HallC7×C11 ⋊ C9×D17
HallC7×C9 ⋊ D187
SylowC17 ⋊ C9×D77
SylowC11 ⋊ C9×D119
SylowC7 ⋊ C9×D187

Subgroups

subgroupG/H
center, hypercenterC9D1309
commutator, hypocenterC7×C11×C17C2×C9
FrattiniC3C3×D1309
FittingC7×C9×C11×C17C2
socle, cosocleC3×C7×C11×C17C2×C3
prime radicalC3×D1309C3
LCSG ▷ C7×C11×C17
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 9);