Finite Group Databasebeta

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C4×C5×C19×C31⋊C3 #47977531

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C19×C31⋊C3
unambiguous semidirect product(C4×C5×C31)⋊(C3×C19)

Splittings

Fitting, HallC4×C5×C19×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C4×C5×C19
HallC5×C19×C31 ⋊ C3×C4
HallC4×C19×C31 ⋊ C3×C5
HallC4×C5×C31 ⋊ C3×C19
HallC19×C31 ⋊ C3×C4×C5
HallC5×C31 ⋊ C3×C4×C19
HallC4×C31 ⋊ C3×C5×C19

Subgroups

subgroupG/H
center, hypercenterC4×C5×C19C31⋊C3
commutator, hypocenterC31C3×C4×C5×C19
FrattiniC2C2×C5×C19×C31⋊C3
FittingC4×C5×C19×C31C3
socleC2×C5×C19×C31C2×C3
prime radicalC2×C5×C19×C31⋊C3C2
cosocleC2×C31C2×C3×C5×C19
LCSG ▷ C31
UCSC1 ◁ C4×C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11780

Conjugacy classes & character table

4940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 3);