Finite Group Databasebeta

← Prev (#46777843) Next (#46777845) →

C5×C17×Dic99 #46777844

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×Dic99
unambiguous semidirect productC9⋊(C5×C17×Dic11)

Splittings

derived, HallC9×C11 ⋊ C4×C5×C17
HallC5×C9×C11×C17 ⋊ C4
HallC9×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ C4×C17
HallC11×C17 ⋊ C5×Dic9
HallC9×C17 ⋊ C5×Dic11
HallC5×C11 ⋊ C17×Dic9
HallC5×C9 ⋊ C17×Dic11
SylowC11 ⋊ C5×C17×Dic9
SylowC9 ⋊ C5×C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17D99
commutator, hypocenterC9×C11C4×C5×C17
FrattiniC2×C3C5×C17×D33
FittingC2×C5×C9×C11×C17C2
socle, prime radicalC2×C3×C5×C11×C17D3
cosocleC2×C9×C11C2×C5×C17
LCSG ▷ C9×C11
UCSC1 ◁ C2×C5×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

8670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 12);