Finite Group Databasebeta

← Prev (#46778026) Next (#46778028) →

C2×C32×C17⋊AGL(1,𝔽11) #46778027

order33660
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C17⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C17)⋊(C32×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C32×D17)
unambiguous semidirect product(C2×D187)⋊(C32×C5)
unambiguous semidirect product(C2×C3×D187)⋊(C3×C5)
unambiguous semidirect product(C2×C32×D187)⋊C5

Splittings

Fitting, socleC2×C32×C11×C17 ⋊ C2×C5
derived, HallC11×C17 ⋊ C22×C32×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallC2×C32×D187 ⋊ C5
HallC32×C11×C17 ⋊ C22×C5
HallC17×C11⋊C5 ⋊ C22×C32
HallC2×D187 ⋊ C32×C5
HallC32×C11⋊C5 ⋊ C2×D17
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC32×C11 ⋊ C2×C5×D17
HallC11⋊C5 ⋊ C2×C32×D17
SylowC17 ⋊ C2×C32×AGL(1,𝔽11)
SylowC11 ⋊ C2×C32×C5×D17

Subgroups

subgroupG/H
center, hypercenterC2×C32C17⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C17C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C11×C17
UCSC1 ◁ C2×C32

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3366

Conjugacy classes & character table

1206 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 195);