Finite Group Databasebeta

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C2×C3×C17×C3⋊AGL(1,𝔽11) #46778029

order33660
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C17×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C3×C17×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D3×C17)
unambiguous semidirect product(C2×D33)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C3×D33)⋊(C5×C17)
unambiguous semidirect product(C2×C17×D33)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C17×D33)⋊C5

Splittings

Fitting, socleC2×C32×C11×C17 ⋊ C2×C5
derivedC3×C11 ⋊ C22×C3×C5×C17
HallC32×C17×C11⋊C5 ⋊ C22
HallC2×C3×C17×D33 ⋊ C5
HallC32×C11×C17 ⋊ C22×C5
HallC17×C11⋊C5 ⋊ C2×C3×D3
HallC32×C11⋊C5 ⋊ C22×C17
HallC2×C3×D33 ⋊ C5×C17
HallC11×C17 ⋊ C2×C3×C5×D3
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC32×C11 ⋊ C22×C5×C17
HallC11⋊C5 ⋊ C2×C3×D3×C17
SylowC11 ⋊ C2×C3×C5×D3×C17
SylowC32 ⋊ C2×C17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C17

176 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 2244

Conjugacy classes & character table

1836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 197);