Finite Group Databasebeta

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C11×D975 #36339693

order21450
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D975
unambiguous semidirect productC3⋊(C11×D325)
unambiguous semidirect productC13⋊(C11×D75)
unambiguous semidirect productC25⋊(C11×D39)

Splittings

Fitting, HallC3×C11×C13×C25 ⋊ C2
derived, HallC3×C13×C25 ⋊ C2×C11
HallC11×C13×C25 ⋊ D3
HallC3×C11×C25 ⋊ D13
HallC3×C11×C13 ⋊ D25
HallC13×C25 ⋊ D3×C11
HallC11×C25 ⋊ D39
HallC11×C13 ⋊ D75
HallC3×C25 ⋊ C11×D13
HallC3×C13 ⋊ C11×D25
HallC3×C11 ⋊ D325
SylowC25 ⋊ C11×D39
SylowC13 ⋊ C11×D75
SylowC3 ⋊ C11×D325

Subgroups

subgroupG/H
center, hypercenterC11D975
commutator, cosocle, hypocenterC3×C13×C25C2×C11
FrattiniC5C11×D195
FittingC3×C11×C13×C25C2
socleC3×C5×C11×C13D5
LCSG ▷ C3×C13×C25
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

5379 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 17);