Finite Group Databasebeta

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C11×C29×D57 #49138309

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

Aliases

direct productC11×C29×D57
unambiguous semidirect productC3⋊(C11×C29×D19)
unambiguous semidirect productC19⋊(D3×C11×C29)

Splittings

Fitting, socle, HallC3×C11×C19×C29 ⋊ C2
derived, HallC3×C19 ⋊ C2×C11×C29
HallC11×C19×C29 ⋊ D3
HallC3×C19×C29 ⋊ C2×C11
HallC3×C11×C29 ⋊ D19
HallC3×C11×C19 ⋊ C2×C29
HallC19×C29 ⋊ D3×C11
HallC11×C19 ⋊ D3×C29
HallC3×C29 ⋊ C11×D19
HallC3×C11 ⋊ C29×D19
SylowC19 ⋊ D3×C11×C29
SylowC3 ⋊ C11×C29×D19

Subgroups

subgroupG/H
center, hypercenterC11×C29D57
commutator, cosocle, hypocenterC3×C19C2×C11×C29
FrattiniC1G
Fitting, socleC3×C11×C19×C29C2
LCSG ▷ C3×C19
UCSC1 ◁ C11×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18183

Conjugacy classes & character table

9570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36366, 12);