Finite Group Databasebeta

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C9×C17×D77 #37555614

order23562
automorphism?
homologyAbelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×D77
unambiguous semidirect productC11⋊(C9×D7×C17)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC7×C11 ⋊ C2×C9×C17
HallC9×C11×C17 ⋊ D7
HallC7×C11×C17 ⋊ C2×C9
HallC7×C9×C17 ⋊ D11
HallC7×C9×C11 ⋊ C2×C17
HallC11×C17 ⋊ C9×D7
HallC7×C17 ⋊ C9×D11
HallC9×C11 ⋊ D7×C17
HallC7×C9 ⋊ C17×D11
SylowC11 ⋊ C9×D7×C17
SylowC7 ⋊ C9×C17×D11

Subgroups

subgroupG/H
center, hypercenterC9×C17D77
commutator, hypocenterC7×C11C2×C9×C17
FrattiniC3C3×C17×D77
FittingC7×C9×C11×C17C2
socleC3×C7×C11×C17C2×C3
prime radicalC3×C17×D77C3
cosocleC3×C7×C11C2×C3×C17
LCSG ▷ C7×C11
UCSC1 ◁ C9×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

6120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 8);