Finite Group Databasebeta

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C9×C17×ΓL(1,𝔽32) #37557331

order23715
automorphism?
homologyAbelianization (H1) = C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×ΓL(1,𝔽32)
unambiguous semidirect product(C9×C31)⋊(C5×C17)
unambiguous semidirect product(C9×C17×C31)⋊C5

Splittings

Fitting, HallC9×C17×C31 ⋊ C5
derived, SylowC31 ⋊ C5×C9×C17
HallC17×C31 ⋊ C5×C9
HallC9×C31 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC9×C17ΓL(1,𝔽32)
commutator, hypocenterC31C5×C9×C17
FrattiniC3C3×C17×ΓL(1,𝔽32)
FittingC9×C17×C31C5
socleC3×C17×C31C3×C5
prime radicalC3×C17×ΓL(1,𝔽32)C3
cosocleC3×C31C3×C5×C17
LCSG ▷ C31
UCSC1 ◁ C9×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4743

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23715, 2);