Finite Group Databasebeta

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C13×C25×C7⋊C9 #35205998

order20475
automorphism?
homologyAbelianization (H1) = C9×C13×C25 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, SylowC7 ⋊ C9×C13×C25
HallC7×C13×C25 ⋊ C9
HallC7×C25 ⋊ C9×C13
HallC7×C13 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C13×C25ΓL(1,𝔽8)
commutator, hypocenterC7C9×C13×C25
FrattiniC3×C5C5×C13×ΓL(1,𝔽8)
FittingC3×C7×C13×C25C3
socle, prime radicalC3×C5×C7×C13C3×C5
cosocleC3×C5×C7C3×C5×C13
LCSG ▷ C7
UCSC1 ◁ C3×C13×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20475

Conjugacy classes & character table

4875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20475, 3);