Finite Group Databasebeta

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D3×C17×C3⋊AGL(1,𝔽11) #46778007

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

Aliases

direct productD3×C17×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C3×D3)⋊(C17×AGL(1,𝔽11))
unambiguous semidirect product(D3×C11⋊C5)⋊(D3×C17)
unambiguous semidirect product(D3×D33)⋊(C5×C17)
unambiguous semidirect product(D3×C17×D33)⋊C5

Splittings

Fitting, socle, HallC32×C11×C17 ⋊ C22×C5
derived, HallC32×C11 ⋊ C22×C5×C17
HallC32×C17×C11⋊C5 ⋊ C22
HallD3×C17×D33 ⋊ C5
HallC17×C11⋊C5 ⋊ D32
HallC32×C11⋊C5 ⋊ C22×C17
HallD3×D33 ⋊ C5×C17
HallC11×C17 ⋊ C5×D32
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D32×C17
SylowC11 ⋊ C5×D32×C17
SylowC32 ⋊ C2×C17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC17D3×C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC32×C11C22×C5×C17
FrattiniC1G
Fitting, socleC32×C11×C17C22×C5
LCSG ▷ C32×C11
UCSC1 ◁ C17

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 1122

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 175);