Finite Group Databasebeta

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C3×C5×C17×C31⋊C3 #37557337

order23715
automorphism?
homologyAbelianization (H1) = C32×C5×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C17×C31⋊C3
unambiguous semidirect product(C5×C31)⋊(C32×C17)
unambiguous semidirect product(C3×C5×C31)⋊(C3×C17)
unambiguous semidirect product(C5×C17×C31)⋊C32
unambiguous semidirect product(C3×C5×C17×C31)⋊C3

Splittings

Fitting, socleC3×C5×C17×C31 ⋊ C3
derived, SylowC31 ⋊ C32×C5×C17
HallC5×C17×C31 ⋊ C32
HallC17×C31 ⋊ C32×C5
HallC5×C31 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17C31⋊C3
commutator, cosocle, hypocenterC31C32×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C31C3
LCSG ▷ C31
UCSC1 ◁ C3×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3315 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23715, 8);