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C2×C3×C3⋊(C17⋊AGL(1,𝔽11)) #46778030

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

Aliases

direct productC2×C3×C3⋊(C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C3×C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C17)⋊(C3×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D51)
unambiguous semidirect product(C2×D561)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D561)⋊C5

Splittings

Fitting, socleC2×C32×C11×C17 ⋊ C2×C5
derivedC3×C11×C17 ⋊ C22×C3×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallC2×C3×D561 ⋊ C5
HallC32×C11×C17 ⋊ C22×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 ⋊ C2×C3×D51
SylowC17 ⋊ C2×C3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C3×C5×D51
SylowC32 ⋊ C2×C17⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C17⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C17C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2×C3

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 36
transitive degreeμt(G) = 2244

A minimal faithful permutation representation — 2 generators on 36 points:

(3,4,5)(7,8)(10,14,15,13,18,11,12,19,16,17)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);(1,2)(6,7,8)(9,10,13,18,12,15,19,14,17,16,11)(20,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22)

Conjugacy classes & character table

1116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 198);