Finite Group Databasebeta

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C9×D7×C41⋊C5 #38788917

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D7×C41⋊C5
unambiguous semidirect product(C9×D7×C41)⋊C5

Splittings

Fitting, HallC7×C9×C41 ⋊ C2×C5
derived, HallC7×C41 ⋊ C2×C5×C9
HallC7×C9×C41⋊C5 ⋊ C2
HallC9×D7×C41 ⋊ C5
HallC7×C41⋊C5 ⋊ C2×C9
HallD7×C41 ⋊ C5×C9
HallC9×C41 ⋊ C5×D7
HallC7×C9 ⋊ C2×C41⋊C5
SylowC41 ⋊ C5×C9×D7
SylowC7 ⋊ C2×C9×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC9D7×C41⋊C5
commutator, hypocenterC7×C41C2×C5×C9
FrattiniC3C3×D7×C41⋊C5
FittingC7×C9×C41C2×C5
socle, cosocleC3×C7×C41C2×C3×C5
prime radicalC3×D7×C41⋊C5C3
LCSG ▷ C7×C41
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 21);