Finite Group Databasebeta

← Prev (#49138298) Next (#49138300) →

C2×C11×C29×C19⋊C3 #49138299

order36366
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C29×C19⋊C3
unambiguous semidirect product(C2×C19)⋊(C3×C11×C29)
unambiguous semidirect product(C2×C11×C19)⋊(C3×C29)
unambiguous semidirect product(C2×C19×C29)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C19×C29)⋊C3

Splittings

Fitting, socle, HallC2×C11×C19×C29 ⋊ C3
derived, SylowC19 ⋊ C2×C3×C11×C29
HallC11×C19×C29 ⋊ C2×C3
HallC2×C19×C29 ⋊ C3×C11
HallC19×C29 ⋊ C2×C3×C11
HallC2×C11×C19 ⋊ C3×C29
HallC11×C19 ⋊ C2×C3×C29
HallC2×C19 ⋊ C3×C11×C29

Subgroups

subgroupG/H
center, hypercenterC2×C11×C29C19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C11×C29
FrattiniC1G
Fitting, socleC2×C11×C19×C29C3
LCSG ▷ C19
UCSC1 ◁ C2×C11×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12122

Conjugacy classes & character table

5742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36366, 2);