Finite Group Databasebeta

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C11×D1335 #44440331

order29370
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1335
unambiguous semidirect productC3⋊(C11×D445)
unambiguous semidirect productC5⋊(C11×D267)

Splittings

Fitting, socle, HallC3×C5×C11×C89 ⋊ C2
derived, HallC3×C5×C89 ⋊ C2×C11
HallC5×C11×C89 ⋊ D3
HallC3×C11×C89 ⋊ D5
HallC11×C89 ⋊ D15
HallC5×C89 ⋊ D3×C11
HallC3×C89 ⋊ D5×C11
HallC3×C5×C11 ⋊ D89
SylowC89 ⋊ C11×D15
HallC5×C11 ⋊ D267
HallC3×C11 ⋊ D445
HallC3×C5 ⋊ C11×D89
SylowC5 ⋊ C11×D267
SylowC3 ⋊ C11×D445

Subgroups

subgroupG/H
center, hypercenterC11D1335
commutator, cosocle, hypocenterC3×C5×C89C2×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C89C2
LCSG ▷ C3×C5×C89
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14685

Conjugacy classes & character table

7359 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 16);