Finite Group Databasebeta

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C11×D15⋊D29 #34062399

order19140
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D15⋊D29
unambiguous semidirect productD15⋊(C11×D29)
unambiguous semidirect productD87⋊(D5×C11)
unambiguous semidirect productD145⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C22
derived, HallC3×C5×C29 ⋊ C22×C11
HallC5×C11×C29 ⋊ C2×D3
HallC3×C11×C29 ⋊ C2×D5
HallC11×C29 ⋊ D3×D5
HallC3×C5×C11 ⋊ C2×D29
HallC5×C29 ⋊ C2×D3×C11
HallC3×C29 ⋊ C2×D5×C11
HallC5×C11 ⋊ D3×D29
HallC3×C11 ⋊ D5×D29
SylowC29 ⋊ D3×D5×C11
HallC3×C5 ⋊ C2×C11×D29
SylowC5 ⋊ D3×C11×D29
SylowC3 ⋊ D5×C11×D29

Subgroups

subgroupG/H
center, hypercenterC11D15⋊D29
commutator, cosocle, hypocenterC3×C5×C29C22×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C29C22
LCSG ▷ C3×C5×C29
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 92);