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C11×C13×D75 #36339692

order21450
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×D75
unambiguous semidirect productC3⋊(C11×C13×D25)
unambiguous semidirect productC25⋊(D3×C11×C13)

Splittings

Fitting, HallC3×C11×C13×C25 ⋊ C2
derived, HallC3×C25 ⋊ C2×C11×C13
HallC11×C13×C25 ⋊ D3
HallC3×C13×C25 ⋊ C2×C11
HallC3×C11×C25 ⋊ C2×C13
HallC3×C11×C13 ⋊ D25
HallC13×C25 ⋊ D3×C11
HallC11×C25 ⋊ D3×C13
HallC3×C13 ⋊ C11×D25
HallC3×C11 ⋊ C13×D25
SylowC25 ⋊ D3×C11×C13
SylowC3 ⋊ C11×C13×D25

Subgroups

subgroupG/H
center, hypercenterC11×C13D75
commutator, cosocle, hypocenterC3×C25C2×C11×C13
FrattiniC5C11×C13×D15
FittingC3×C11×C13×C25C2
socleC3×C5×C11×C13D5
LCSG ▷ C3×C25
UCSC1 ◁ C11×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

5577 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 16);