Finite Group Databasebeta

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C9×#11717961⋊C5 #49146776

order36900
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#11717961⋊C5
unambiguous semidirect product#11717961⋊(C5×C9)
unambiguous semidirect product(C9×#11717961)⋊C5

Splittings

FittingC5×C9×C41 ⋊ C4×C5
derivedC5×C41 ⋊ C4×C5×C9
HallC5×C9×C41⋊C5 ⋊ C4
HallC5×C41⋊C5 ⋊ C4×C9
HallC9×C41 ⋊ C5×AGL(1,𝔽5)
SylowC41 ⋊ C5×C9×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC9#11717961⋊C5
commutator, hypocenterC5×C41C4×C5×C9
FrattiniC3C3×#11717961⋊C5
FittingC5×C9×C41C4×C5
socleC3×C5×C41C3×C4×C5
prime radicalC3×C5⋊(D41⋊C5)C2×C3
cosocleC3×D205C2×C3×C5
LCSG ▷ C5×C41
UCSC1 ◁ C9

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1845

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 177);