Finite Group Databasebeta

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C9×Dic1045 #49178302

order37620
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic1045
unambiguous semidirect productC11⋊(C9×Dic95)

Splittings

derived, HallC5×C11×C19 ⋊ C4×C9
HallC5×C9×C11×C19 ⋊ C4
HallC9×C11×C19 ⋊ Dic5
HallC5×C9×C19 ⋊ Dic11
HallC5×C9×C11 ⋊ Dic19
HallC11×C19 ⋊ C9×Dic5
HallC9×C19 ⋊ Dic55
HallC9×C11 ⋊ Dic95
HallC5×C19 ⋊ C9×Dic11
HallC5×C11 ⋊ C9×Dic19
HallC5×C9 ⋊ Dic209
SylowC19 ⋊ C9×Dic55
SylowC11 ⋊ C9×Dic95
SylowC5 ⋊ C9×Dic209

Subgroups

subgroupG/H
center, hypercenterC2×C9D1045
commutator, hypocenterC5×C11×C19C4×C9
FrattiniC2×C3C3×D1045
FittingC2×C5×C9×C11×C19C2
socle, prime radical, cosocleC2×C3×C5×C11×C19C2×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C2×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 11);