Finite Group Databasebeta

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C17×D693 #37555622

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

Aliases

direct productC17×D693
unambiguous semidirect productC7⋊(C17×D99)
unambiguous semidirect productC9⋊(C17×D77)
unambiguous semidirect productC11⋊(C17×D63)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC7×C9×C11 ⋊ C2×C17
HallC9×C11×C17 ⋊ D7
HallC7×C11×C17 ⋊ D9
HallC7×C9×C17 ⋊ D11
HallC11×C17 ⋊ D63
HallC9×C17 ⋊ D77
HallC7×C17 ⋊ D99
HallC9×C11 ⋊ D7×C17
HallC7×C11 ⋊ C17×D9
HallC7×C9 ⋊ C17×D11
SylowC11 ⋊ C17×D63
SylowC9 ⋊ C17×D77
SylowC7 ⋊ C17×D99

Subgroups

subgroupG/H
center, hypercenterC17D693
commutator, cosocle, hypocenterC7×C9×C11C2×C17
FrattiniC3C17×D231
FittingC7×C9×C11×C17C2
socleC3×C7×C11×C17D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 16);