Finite Group Databasebeta

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C17×C22⋊(C31⋊C9) #34039030

order18972
automorphism?
homologyAbelianization (H1) = C9×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×C22⋊(C31⋊C9)
unambiguous semidirect productC22⋊(C17×C31⋊C9)
unambiguous semidirect productC31⋊(C17×C22⋊C9)
unambiguous semidirect product(C22×C17)⋊(C31⋊C9)
unambiguous semidirect product(C17×C31)⋊(C22⋊C9)

Splittings

derived, HallC22×C31 ⋊ C9×C17
HallC22×C17×C31 ⋊ C9
HallC17×C31 ⋊ C22⋊C9
HallC22×C17 ⋊ C31⋊C9
SylowC31 ⋊ C17×C22⋊C9
SylowC22 ⋊ C17×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C17C22⋊(C31⋊C3)
commutator, hypocenterC22×C31C9×C17
FrattiniC3C17×C22⋊(C31⋊C3)
Fitting, socle, prime radicalC22×C3×C17×C31C3
cosocleC22×C3×C31C3×C17
LCSG ▷ C22×C31
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9486

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18972, 33);