Finite Group Databasebeta

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C3×C11×D551 #49138302

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

Aliases

direct productC3×C11×D551
unambiguous semidirect productC29⋊(C3×C11×D19)

Splittings

Fitting, socle, HallC3×C11×C19×C29 ⋊ C2
derived, HallC19×C29 ⋊ C2×C3×C11
HallC11×C19×C29 ⋊ C2×C3
HallC3×C19×C29 ⋊ C2×C11
HallC3×C11×C29 ⋊ D19
HallC3×C11×C19 ⋊ D29
HallC11×C29 ⋊ C3×D19
HallC11×C19 ⋊ C3×D29
HallC3×C29 ⋊ C11×D19
HallC3×C19 ⋊ C11×D29
SylowC29 ⋊ C3×C11×D19
SylowC19 ⋊ C3×C11×D29

Subgroups

subgroupG/H
center, hypercenterC3×C11D551
commutator, cosocle, hypocenterC19×C29C2×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C19×C29C2
LCSG ▷ C19×C29
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18183

Conjugacy classes & character table

9141 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36366, 5);