Finite Group Databasebeta

← Prev (#46777844) Next (#46777846) →

C5×Dic1683 #46777845

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

Aliases

direct productC5×Dic1683
unambiguous semidirect productC9⋊(C5×Dic187)

Splittings

derived, HallC9×C11×C17 ⋊ C4×C5
HallC5×C9×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ Dic17
HallC11×C17 ⋊ C5×Dic9
HallC9×C17 ⋊ C5×Dic11
HallC9×C11 ⋊ C5×Dic17
HallC5×C17 ⋊ Dic99
HallC5×C11 ⋊ Dic153
HallC5×C9 ⋊ Dic187
SylowC17 ⋊ C5×Dic99
SylowC11 ⋊ C5×Dic153
SylowC9 ⋊ C5×Dic187

Subgroups

subgroupG/H
center, hypercenterC2×C5D1683
commutator, hypocenterC9×C11×C17C4×C5
FrattiniC2×C3C5×D561
FittingC2×C5×C9×C11×C17C2
socle, prime radicalC2×C3×C5×C11×C17D3
cosocleC2×C9×C11×C17C2×C5
LCSG ▷ C9×C11×C17
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

8430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 13);