Finite Group Databasebeta

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C5×C17×C22⋊(C31⋊C3) #44539395

order31620
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC5×C17×C22⋊(C31⋊C3)
unambiguous semidirect productC22⋊(C5×C17×C31⋊C3)
unambiguous semidirect product(C22×C5)⋊(C17×C31⋊C3)
unambiguous semidirect product(C22×C17)⋊(C5×C31⋊C3)
unambiguous semidirect product(C5×C31)⋊(A4×C17)
unambiguous semidirect product(C22×C5×C17)⋊(C31⋊C3)
unambiguous semidirect product(C5×C17×C31)⋊A4

Splittings

Fitting, socle, HallC22×C5×C17×C31 ⋊ C3
derived, HallC22×C31 ⋊ C3×C5×C17
HallC5×C17×C31 ⋊ A4
HallC22×C17×C31 ⋊ C3×C5
HallC22×C5×C31 ⋊ C3×C17
HallC17×C31 ⋊ C5×A4
HallC22×C5×C17 ⋊ C31⋊C3
HallC5×C31 ⋊ A4×C17
HallC22×C17 ⋊ C5×C31⋊C3
SylowC31 ⋊ C5×A4×C17
HallC22×C5 ⋊ C17×C31⋊C3
SylowC22 ⋊ C5×C17×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C17C22⋊(C31⋊C3)
commutator, cosocle, hypocenterC22×C31C3×C5×C17
FrattiniC1G
Fitting, socleC22×C5×C17×C31C3
LCSG ▷ C22×C31
UCSC1 ◁ C5×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10540

Conjugacy classes & character table

3740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 152);