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AGL(1,𝔽11)×C3⋊D51 #46778020

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

Aliases

direct productAGL(1,𝔽11)×C3⋊D51
unambiguous semidirect productD11⋊(C5×C3⋊D51)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊D51
unambiguous semidirect product(C17×AGL(1,𝔽11))⋊(C3⋊D3)
unambiguous semidirect product(D11×C3⋊D51)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C17 ⋊ C22×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallD11×C3⋊D51 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×C3⋊D3
HallC32×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×C3⋊D3
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC32×C11 ⋊ C2×C5×D17
HallC11⋊C5 ⋊ C2×C3⋊D51
SylowC17 ⋊ C3⋊D3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C3⋊D51
SylowC32 ⋊ D17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C17C22×C5
LCSG ▷ C32×C11×C17
UCSC1

240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 1683

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 188);