Finite Group Databasebeta

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C3×C11×D475 #44535436

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D475
unambiguous semidirect productC25⋊(C3×C11×D19)

Splittings

Fitting, HallC3×C11×C19×C25 ⋊ C2
derived, HallC19×C25 ⋊ C2×C3×C11
HallC11×C19×C25 ⋊ C2×C3
HallC3×C19×C25 ⋊ C2×C11
HallC3×C11×C25 ⋊ D19
HallC3×C11×C19 ⋊ D25
HallC11×C25 ⋊ C3×D19
HallC11×C19 ⋊ C3×D25
HallC3×C25 ⋊ C11×D19
HallC3×C19 ⋊ C11×D25
SylowC25 ⋊ C3×C11×D19
SylowC19 ⋊ C3×C11×D25

Subgroups

subgroupG/H
center, hypercenterC3×C11D475
commutator, cosocle, hypocenterC19×C25C2×C3×C11
FrattiniC5C3×C11×D95
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19D5
LCSG ▷ C19×C25
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7887 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 9);