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AGL(1,𝔽11)×D147 #44568342

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

Aliases

direct productAGL(1,𝔽11)×D147
unambiguous semidirect productD11⋊(C5×D147)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊D49
unambiguous semidirect product(C49×AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D11×D147)⋊C5

Splittings

Fitting, derived, HallC3×C11×C49 ⋊ C22×C5
HallC3×C49×C11⋊C5 ⋊ C22
HallD11×D147 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×D3
HallC11×C49 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D49
HallC3×C49 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D147
SylowC49 ⋊ D3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C2×C5×D147
SylowC3 ⋊ D49×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C11×C49C22×C5
FrattiniC7D21×AGL(1,𝔽11)
socleC3×C7×C11C2×C5×D7
LCSG ▷ C3×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 37 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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 44);