Finite Group Databasebeta

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C9×C7⋊#10596817 #49141259

order36540
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊#10596817

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C4
derived, HallC5×C7×C29 ⋊ C4×C9
HallC7×C9×C29 ⋊ Dic5
HallC5×C9×C29 ⋊ Dic7
HallC5×C7×C9 ⋊ #1181
HallC9×C29 ⋊ Dic35
HallC7×C29 ⋊ C9×Dic5
HallC5×C29 ⋊ C9×Dic7
HallC7×C9 ⋊ #10596817
HallC5×C9 ⋊ C7⋊#1181
HallC5×C7 ⋊ C9×#1181
SylowC29 ⋊ C9×Dic35
SylowC7 ⋊ C9×#10596817
SylowC5 ⋊ C9×C7⋊#1181

Subgroups

subgroupG/H
center, hypercenterC9C7⋊#10596817
commutator, hypocenterC5×C7×C29C4×C9
FrattiniC3C3×C7⋊#10596817
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29C3×C4
prime radical, cosocleC3×C5×C7×D29C2×C3
LCSG ▷ C5×C7×C29
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

2547 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 101);