Finite Group Databasebeta

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C13×C25×D33 #36339690

order21450
automorphism?
homologyAbelianization (H1) = C2×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC13×C25×D33
unambiguous semidirect productC3⋊(C13×D11×C25)

Splittings

Fitting, HallC3×C11×C13×C25 ⋊ C2
derived, HallC3×C11 ⋊ C2×C13×C25
HallC11×C13×C25 ⋊ D3
HallC3×C13×C25 ⋊ D11
HallC3×C11×C25 ⋊ C2×C13
HallC3×C11×C13 ⋊ C2×C25
HallC11×C25 ⋊ D3×C13
HallC11×C13 ⋊ D3×C25
HallC3×C25 ⋊ C13×D11
HallC3×C13 ⋊ D11×C25
SylowC11 ⋊ D3×C13×C25
SylowC3 ⋊ C13×D11×C25

Subgroups

subgroupG/H
center, hypercenterC13×C25D33
commutator, hypocenterC3×C11C2×C13×C25
FrattiniC5C5×C13×D33
FittingC3×C11×C13×C25C2
socleC3×C5×C11×C13C2×C5
prime radicalC5×C13×D33C5
cosocleC3×C5×C11C2×C5×C13
LCSG ▷ C3×C11
UCSC1 ◁ C13×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 14);