Finite Group Databasebeta

← Prev (#49178357) Next (#49178359) →

C2×C9⋊(C19⋊AGL(1,𝔽11)) #49178358

order37620
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C9)⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C19)⋊(C9⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D171
unambiguous semidirect product(C2×D1881)⋊C5

Splittings

FittingC2×C9×C11×C19 ⋊ C2×C5
derived, HallC9×C11×C19 ⋊ C22×C5
HallC9×C19×C11⋊C5 ⋊ C22
HallC2×D1881 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×D9
HallC9×C11⋊C5 ⋊ C2×D19
HallC11×C19 ⋊ C2×C5×D9
HallC9×C19 ⋊ C2×AGL(1,𝔽11)
HallC9×C11 ⋊ C2×C5×D19
HallC11⋊C5 ⋊ C2×D171
SylowC19 ⋊ C2×C9⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D171
SylowC9 ⋊ C2×C19⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(C19⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC9×C11×C19C22×C5
FrattiniC3C2×C3⋊(C19⋊AGL(1,𝔽11))
FittingC2×C9×C11×C19C2×C5
socleC2×C3×C11×C19C5×D3
LCSG ▷ C9×C11×C19
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 3762

A minimal faithful permutation representation — 2 generators on 41 points:

(4,6)(5,9)(7,8)(10,11)(13,17,18,16,21,14,15,22,19,20)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41);(1,2)(3,11,6,9,8,7,5,4,10)(12,13,16,21,15,18,22,17,20,19,14)(23,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25)

Conjugacy classes & character table

1212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 67);