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C32×D17×AGL(1,𝔽11) #46777997

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

Aliases

direct productC32×D17×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C32×C5×D17)
unambiguous semidirect product(D11×D17)⋊(C32×C5)
unambiguous semidirect product(D17×C11⋊C5)⋊(C2×C32)
unambiguous semidirect product(C17×AGL(1,𝔽11))⋊(C2×C32)
unambiguous semidirect product(C17⋊AGL(1,𝔽11))⋊(C2×C32)
unambiguous semidirect product(C3×D11×D17)⋊(C3×C5)
unambiguous semidirect product(C32×D11×D17)⋊C5

Splittings

Fitting, socle, HallC32×C11×C17 ⋊ C22×C5
derived, HallC11×C17 ⋊ C22×C32×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallC32×D11×D17 ⋊ C5
HallC17×C11⋊C5 ⋊ C22×C32
HallD11×D17 ⋊ 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, hypercenterC32D17×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C17C22×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C17C22×C5
LCSG ▷ C11×C17
UCSC1 ◁ C32

240 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1683

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 165);