Finite Group Databasebeta

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C9×Dic935 #46777841

order33660
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic935
unambiguous semidirect productC11⋊(C9×Dic85)

Splittings

derived, HallC5×C11×C17 ⋊ C4×C9
HallC5×C9×C11×C17 ⋊ C4
HallC9×C11×C17 ⋊ Dic5
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ Dic17
HallC11×C17 ⋊ C9×Dic5
HallC9×C17 ⋊ Dic55
HallC9×C11 ⋊ Dic85
HallC5×C17 ⋊ C9×Dic11
HallC5×C11 ⋊ C9×Dic17
HallC5×C9 ⋊ Dic187
SylowC17 ⋊ C9×Dic55
SylowC11 ⋊ C9×Dic85
SylowC5 ⋊ C9×Dic187

Subgroups

subgroupG/H
center, hypercenterC2×C9D935
commutator, hypocenterC5×C11×C17C4×C9
FrattiniC2×C3C3×D935
FittingC2×C5×C9×C11×C17C2
socle, prime radical, cosocleC2×C3×C5×C11×C17C2×C3
LCSG ▷ C5×C11×C17
UCSC1 ◁ C2×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

8442 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 9);