Finite Group Databasebeta

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C19×D15×C11⋊C5 #44535486

order31350
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D15×C11⋊C5
unambiguous semidirect productC3⋊(D5×C19×C11⋊C5)
unambiguous semidirect productC5⋊(D3×C19×C11⋊C5)
unambiguous semidirect product(C11×D15)⋊(C5×C19)
unambiguous semidirect product(C11×C19×D15)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C5
derivedC3×C5×C11 ⋊ C2×C5×C19
HallC3×C5×C19×C11⋊C5 ⋊ C2
HallC5×C19×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ C2×C19
HallC3×C11×C19 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D3×C19
HallC11×C19 ⋊ C5×D15
HallC3×C19 ⋊ D5×C11⋊C5
HallC3×C11 ⋊ C5×D5×C19
SylowC11 ⋊ C5×C19×D15
SylowC3 ⋊ D5×C19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC19D15×C11⋊C5
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C19
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 59);