Finite Group Databasebeta

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C11×C25×D13⋊C3 #36339703

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×D13⋊C3
unambiguous semidirect productD13⋊(C3×C11×C25)
unambiguous semidirect product(C13⋊C3)⋊(C2×C11×C25)
unambiguous semidirect product(C25×D13)⋊(C3×C11)
unambiguous semidirect product(C11×C25×D13)⋊C3

Splittings

Fitting, HallC11×C13×C25 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C11×C25
HallC11×C25×C13⋊C3 ⋊ C2
HallC11×C25×D13 ⋊ C3
HallC25×C13⋊C3 ⋊ C2×C11
HallC25×D13 ⋊ C3×C11
HallC11×C13⋊C3 ⋊ C2×C25
HallC13×C25 ⋊ C2×C3×C11
HallC11×D13 ⋊ C3×C25
HallC11×C13 ⋊ C2×C3×C25
HallC13⋊C3 ⋊ C2×C11×C25
HallD13 ⋊ C3×C11×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25D13⋊C3
commutator, hypocenterC13C2×C3×C11×C25
FrattiniC5C5×C11×D13⋊C3
FittingC11×C13×C25C2×C3
socleC5×C11×C13C2×C3×C5
prime radicalC5×C11×D13⋊C3C5
cosocleC5×C13C2×C3×C5×C11
LCSG ▷ C13
UCSC1 ◁ C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3575

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 27);