Finite Group Databasebeta

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C7×C25×C13⋊C9 #35205997

order20475
automorphism?
homologyAbelianization (H1) = C7×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×C13⋊C9
unambiguous semidirect productC13⋊(C7×C9×C25)
unambiguous semidirect product(C13×C25)⋊(C7×C9)

Splittings

derived, SylowC13 ⋊ C7×C9×C25
HallC7×C13×C25 ⋊ C9
HallC13×C25 ⋊ C7×C9
HallC7×C13 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C7×C25C13⋊C3
commutator, hypocenterC13C7×C9×C25
FrattiniC3×C5C5×C7×C13⋊C3
FittingC3×C7×C13×C25C3
socle, prime radicalC3×C5×C7×C13C3×C5
cosocleC3×C5×C13C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C3×C7×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20475

Conjugacy classes & character table

3675 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20475, 2);