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D3×C47⋊AGL(1,𝔽11) #44526627

order31020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C47⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C47)⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C11⋊C5)⋊D47
unambiguous semidirect product(D3×D517)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C47 ⋊ C22×C5
HallC3×C47×C11⋊C5 ⋊ C22
HallD3×D517 ⋊ C5
HallC47×C11⋊C5 ⋊ C2×D3
HallC11×C47 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D47
HallC3×C47 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D3×D47
SylowC47 ⋊ D3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D47
SylowC11 ⋊ C5×D3×D47
SylowC3 ⋊ C2×C47⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C47C22×C5
LCSG ▷ C3×C11×C47
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 1551

A minimal faithful permutation representation — 2 generators on 61 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 30);