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C3×C13×D275 #36339686

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D275
unambiguous semidirect productC11⋊(C3×C13×D25)
unambiguous semidirect productC25⋊(C3×C13×D11)

Splittings

Fitting, HallC3×C11×C13×C25 ⋊ C2
derived, HallC11×C25 ⋊ C2×C3×C13
HallC11×C13×C25 ⋊ C2×C3
HallC3×C13×C25 ⋊ D11
HallC3×C11×C25 ⋊ C2×C13
HallC3×C11×C13 ⋊ D25
HallC13×C25 ⋊ C3×D11
HallC11×C13 ⋊ C3×D25
HallC3×C25 ⋊ C13×D11
HallC3×C11 ⋊ C13×D25
SylowC25 ⋊ C3×C13×D11
SylowC11 ⋊ C3×C13×D25

Subgroups

subgroupG/H
center, hypercenterC3×C13D275
commutator, cosocle, hypocenterC11×C25C2×C3×C13
FrattiniC5C3×C13×D55
FittingC3×C11×C13×C25C2
socleC3×C5×C11×C13D5
LCSG ▷ C11×C25
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

5421 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 10);