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AGL(1,𝔽11)×D129 #43248798

order28380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽11)×D129
unambiguous semidirect productD11⋊(C5×D129)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊D43
unambiguous semidirect product(C43×AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D11×D129)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C43 ⋊ C22×C5
HallC3×C43×C11⋊C5 ⋊ C22
HallD11×D129 ⋊ C5
HallC43×C11⋊C5 ⋊ C2×D3
HallC11×C43 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D43
HallC3×C43 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D129
SylowC43 ⋊ D3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D43
SylowC11 ⋊ C2×C5×D129
SylowC3 ⋊ D43×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C43C22×C5
LCSG ▷ C3×C11×C43
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 1419

A minimal faithful permutation representation — 2 generators on 57 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 45);