Finite Group Databasebeta

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C7×C9⋊#10596816 #49141276

order36540
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9⋊#10596816
unambiguous semidirect productC9⋊(C7×#10596816)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C4
derived, HallC5×C9×C29 ⋊ C4×C7
HallC7×C9×C29 ⋊ AGL(1,𝔽5)
HallC5×C7×C29 ⋊ Dic9
HallC5×C7×C9 ⋊ Dic29
HallC9×C29 ⋊ C7×AGL(1,𝔽5)
HallC7×C29 ⋊ C9⋊AGL(1,𝔽5)
HallC5×C29 ⋊ C7×Dic9
HallC7×C9 ⋊ #10596816
HallC5×C9 ⋊ C7×Dic29
HallC5×C7 ⋊ Dic261
SylowC29 ⋊ C7×C9⋊AGL(1,𝔽5)
SylowC9 ⋊ C7×#10596816
SylowC5 ⋊ C7×Dic261

Subgroups

subgroupG/H
center, hypercenterC7C9⋊#10596816
commutator, hypocenterC5×C9×C29C4×C7
FrattiniC3C7×C3⋊#10596816
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29Dic3
prime radicalC3×C7×D5×C29D3
cosocleC9×D5×C29C2×C7
LCSG ▷ C5×C9×C29
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

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(36540, 118);