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C2×C3⋊(C47⋊AGL(1,𝔽11)) #44526635

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

Aliases

direct productC2×C3⋊(C47⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C47⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C47)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D141
unambiguous semidirect product(C2×D1551)⋊C5

Splittings

Fitting, socleC2×C3×C11×C47 ⋊ C2×C5
derived, HallC3×C11×C47 ⋊ C22×C5
HallC3×C47×C11⋊C5 ⋊ C22
HallC2×D1551 ⋊ C5
HallC47×C11⋊C5 ⋊ C2×D3
HallC11×C47 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D47
HallC3×C47 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D141
SylowC47 ⋊ C2×C3⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D47
SylowC11 ⋊ C2×C5×D141
SylowC3 ⋊ C2×C47⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C47⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C47C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C47C2×C5
LCSG ▷ C3×C11×C47
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 3102

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

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

Conjugacy classes & character table

1002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 38);