Finite Group Databasebeta

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C4×C5×C17×C31⋊C3 #44539246

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C17×C31⋊C3
unambiguous semidirect product(C4×C5×C31)⋊(C3×C17)
unambiguous semidirect product(C4×C5×C17×C31)⋊C3

Splittings

Fitting, HallC4×C5×C17×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C4×C5×C17
HallC5×C17×C31 ⋊ C3×C4
HallC4×C17×C31 ⋊ C3×C5
HallC4×C5×C31 ⋊ C3×C17
HallC17×C31 ⋊ C3×C4×C5
HallC5×C31 ⋊ C3×C4×C17
HallC4×C31 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C5×C17C31⋊C3
commutator, hypocenterC31C3×C4×C5×C17
FrattiniC2C2×C5×C17×C31⋊C3
FittingC4×C5×C17×C31C3
socleC2×C5×C17×C31C2×C3
prime radicalC2×C5×C17×C31⋊C3C2
cosocleC2×C31C2×C3×C5×C17
LCSG ▷ C31
UCSC1 ◁ C4×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10540

Conjugacy classes & character table

4420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 3);