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C3×D3×C17⋊AGL(1,𝔽11) #46778003

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

Aliases

direct productC3×D3×C17⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C17)⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(D3×C11⋊C5)⋊(C3×D17)
unambiguous semidirect product(D3×D187)⋊(C3×C5)
unambiguous semidirect product(C3×D3×D187)⋊C5

Splittings

Fitting, socle, HallC32×C11×C17 ⋊ C22×C5
derivedC3×C11×C17 ⋊ C22×C3×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallC3×D3×D187 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×C3×D3
HallC32×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C2×C3×C5×D3
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC32×C11 ⋊ C2×C5×D17
HallC11⋊C5 ⋊ C3×D3×D17
SylowC17 ⋊ C3×D3×AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D3×D17
SylowC32 ⋊ C2×C17⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3D3×C17⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11×C17C22×C3×C5
FrattiniC1G
Fitting, socleC32×C11×C17C22×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C3

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

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1122

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3)(4,5,6)(8,12,13,11,16,9,10,17,14,15)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);(5,6)(7,8,11,16,10,13,17,12,15,14,9)(18,19,21,23,25,27,29,31,33,34,32,30,28,26,24,22,20)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 171);