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C25×C11⋊(D13⋊C3) #36339705

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

Aliases

direct productC25×C11⋊(D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D11×C25)
unambiguous semidirect product(C25×D143)⋊C3

Splittings

Fitting, HallC11×C13×C25 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C25
HallC11×C25×C13⋊C3 ⋊ C2
HallC25×D143 ⋊ C3
HallC25×C13⋊C3 ⋊ D11
HallC11×C13⋊C3 ⋊ C2×C25
HallC13×C25 ⋊ C3×D11
HallD143 ⋊ C3×C25
HallC11×C25 ⋊ D13⋊C3
HallC13⋊C3 ⋊ D11×C25
SylowC13 ⋊ C3×D11×C25
SylowC11 ⋊ C25×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC25C11⋊(D13⋊C3)
commutator, hypocenterC11×C13C2×C3×C25
FrattiniC5C5×C11⋊(D13⋊C3)
FittingC11×C13×C25C2×C3
socle, cosocleC5×C11×C13C2×C3×C5
prime radicalC5×C11⋊(D13⋊C3)C5
LCSG ▷ C11×C13
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3575

Conjugacy classes & character table

1075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 29);