Finite Group Databasebeta

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C7×D9×C41⋊C5 #38788919

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D9×C41⋊C5
unambiguous semidirect productC9⋊(C2×C7×C41⋊C5)
unambiguous semidirect product(D9×C41)⋊(C5×C7)
unambiguous semidirect product(C7×D9×C41)⋊C5

Splittings

Fitting, HallC7×C9×C41 ⋊ C2×C5
derived, HallC9×C41 ⋊ C2×C5×C7
HallC7×C9×C41⋊C5 ⋊ C2
HallC7×D9×C41 ⋊ C5
HallC9×C41⋊C5 ⋊ C2×C7
HallD9×C41 ⋊ C5×C7
HallC7×C41 ⋊ C5×D9
HallC7×C9 ⋊ C2×C41⋊C5
SylowC41 ⋊ C5×C7×D9
SylowC9 ⋊ C2×C7×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC7D9×C41⋊C5
commutator, cosocle, hypocenterC9×C41C2×C5×C7
FrattiniC3D3×C7×C41⋊C5
FittingC7×C9×C41C2×C5
socleC3×C7×C41C5×D3
LCSG ▷ C9×C41
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 23);