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D3×C49⋊AGL(1,𝔽11) #44568344

order32340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C49⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C49)⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C11⋊C5)⋊D49
unambiguous semidirect product(D3×D539)⋊C5

Splittings

Fitting, derived, HallC3×C11×C49 ⋊ C22×C5
HallC3×C49×C11⋊C5 ⋊ C22
HallD3×D539 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×D3
HallC11×C49 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D49
HallC3×C49 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D3×D49
SylowC49 ⋊ D3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C5×D3×D49
SylowC3 ⋊ C2×C49⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C11×C49C22×C5
FrattiniC7D3×C7⋊AGL(1,𝔽11)
socleC3×C7×C11C2×C5×D7
LCSG ▷ C3×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 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) = 63
transitive degreeμt(G) = 1617

A minimal faithful permutation representation — 2 generators on 63 points:

(2,6,7,5,10,3,4,11,8,9)(13,15)(14,18)(16,21)(17,24)(19,27)(20,26)(22,31)(23,34)(25,36)(28,40)(29,39)(30,38)(32,33)(35,45)(37,47)(41,48)(42,50)(43,49)(44,53)(46,55)(51,56)(52,57)(54,59)(58,60)(61,62,63);(1,2,5,10,4,7,11,6,9,8,3)(12,48,23,57,43,45,29,18,37,16,60,31,55,20,27,25,38,54,32,51,15,40,17,50,44,53,42,24,28,13,56,33,59,30,36,19,26,46,22,58,21,47,14,39,35,49,52,34,41)(62,63)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 46);