Finite Group Databasebeta

← Prev (#46777966) Next (#46777968) →

C17×C3⋊Dic165 #46777967

order33660
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC17×C3⋊Dic165
unambiguous semidirect productC3⋊(C17×Dic165)
unambiguous semidirect productC11⋊(C17×C3⋊Dic15)

Splittings

derived, HallC32×C5×C11 ⋊ C4×C17
HallC32×C5×C11×C17 ⋊ C4
HallC32×C11×C17 ⋊ Dic5
HallC5×C11×C17 ⋊ C3⋊Dic3
HallC32×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ C3⋊Dic15
HallC32×C17 ⋊ Dic55
HallC32×C11 ⋊ C17×Dic5
HallC5×C17 ⋊ C3⋊Dic33
HallC5×C11 ⋊ C17×C3⋊Dic3
HallC32×C5 ⋊ C17×Dic11
SylowC11 ⋊ C17×C3⋊Dic15
SylowC32 ⋊ C17×Dic55
SylowC5 ⋊ C17×C3⋊Dic33

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊D165
commutator, hypocenterC32×C5×C11C4×C17
FrattiniC2C17×C3⋊D165
Fitting, socle, prime radicalC2×C32×C5×C11×C17C2
cosocleC2×C32×C5×C11C2×C17
LCSG ▷ C32×C5×C11
UCSC1 ◁ C2×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

8466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 135);