Finite Group Databasebeta

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C11×C29⋊(D19⋊C3) #49138317

order36366
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C29⋊(D19⋊C3)
unambiguous semidirect productC29⋊(C11×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C11×D29)
unambiguous semidirect productD551⋊(C3×C11)
unambiguous semidirect product(C11×D551)⋊C3

Splittings

Fitting, socle, HallC11×C19×C29 ⋊ C2×C3
derived, HallC19×C29 ⋊ C2×C3×C11
HallC11×C29×C19⋊C3 ⋊ C2
HallC11×D551 ⋊ C3
HallC29×C19⋊C3 ⋊ C2×C11
HallD551 ⋊ C3×C11
HallC11×C19⋊C3 ⋊ D29
HallC11×C29 ⋊ D19⋊C3
HallC11×C19 ⋊ C3×D29
HallC19⋊C3 ⋊ C11×D29
SylowC29 ⋊ C11×D19⋊C3
SylowC19 ⋊ C3×C11×D29

Subgroups

subgroupG/H
center, hypercenterC11C29⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C29C2×C3×C11
FrattiniC1G
Fitting, socleC11×C19×C29C2×C3
LCSG ▷ C19×C29
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6061

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36366, 20);