Finite Group Databasebeta

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C11×D1425 #44535444

order31350
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1425
unambiguous semidirect productC3⋊(C11×D475)
unambiguous semidirect productC19⋊(C11×D75)
unambiguous semidirect productC25⋊(C11×D57)

Splittings

Fitting, HallC3×C11×C19×C25 ⋊ C2
derived, HallC3×C19×C25 ⋊ C2×C11
HallC11×C19×C25 ⋊ D3
HallC3×C11×C25 ⋊ D19
HallC3×C11×C19 ⋊ D25
HallC19×C25 ⋊ D3×C11
HallC11×C25 ⋊ D57
HallC11×C19 ⋊ D75
HallC3×C25 ⋊ C11×D19
HallC3×C19 ⋊ C11×D25
HallC3×C11 ⋊ D475
SylowC25 ⋊ C11×D57
SylowC19 ⋊ C11×D75
SylowC3 ⋊ C11×D475

Subgroups

subgroupG/H
center, hypercenterC11D1425
commutator, cosocle, hypocenterC3×C19×C25C2×C11
FrattiniC5C11×D285
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19D5
LCSG ▷ C3×C19×C25
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 17);