Finite Group Databasebeta

← Prev (#44568342) Next (#44568344) →

D49×C3⋊AGL(1,𝔽11) #44568343

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

Aliases

direct productD49×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C3×D49)⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5×D49)⋊D3
unambiguous semidirect product(D33×D49)⋊C5

Splittings

Fitting, derived, HallC3×C11×C49 ⋊ C22×C5
HallC3×C49×C11⋊C5 ⋊ C22
HallD33×D49 ⋊ 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 ⋊ C2×C3⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C5×D3×D49
SylowC3 ⋊ D49×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C11×C49C22×C5
FrattiniC7D7×C3⋊AGL(1,𝔽11)
socleC3×C7×C11C2×C5×D7
LCSG ▷ C3×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 34 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)(13,14)(15,20,38,59,58,37,18,17,28,51,62,48,24,23,22,40,61,56,34,33,32,31,53,54,46,35,45,44,43,42,41,25,47,55,52,30,29,19,36,57,60,39,21,16,26,49,63,50,27);(1,2,5,10,4,7,11,6,9,8,3)(12,13,14)(16,18)(17,21)(19,24)(20,27)(22,30)(23,29)(25,34)(26,37)(28,39)(31,43)(32,42)(33,41)(35,46)(36,48)(38,50)(40,52)(44,53)(45,54)(47,56)(49,58)(51,60)(55,61)(57,62)(59,63)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 45);