Finite Group Databasebeta

← Prev (#31798276) Next (#31798278) →

C2×C11⋊(ΓL(1,𝔽8)⋊D19) #31798277

order17556
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊(ΓL(1,𝔽8)⋊D19)
unambiguous semidirect product(C2×C11)⋊(ΓL(1,𝔽8)⋊D19)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊D209

Splittings

Fitting, socleC2×C7×C11×C19 ⋊ C2×C3
derived, HallC7×C11×C19 ⋊ C22×C3
HallC2×D1463 ⋊ C3
HallC11×C19×ΓL(1,𝔽8) ⋊ C22
HallC19×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D19
HallC11×C19 ⋊ C2×AGL(1,𝔽7)
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D19
HallΓL(1,𝔽8) ⋊ C2×D209
SylowC19 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×ΓL(1,𝔽8)⋊D19
SylowC7 ⋊ C2×C3×D209

Subgroups

subgroupG/H
center, hypercenterC2C11⋊(ΓL(1,𝔽8)⋊D19)
commutator, cosocle, hypocenterC7×C11×C19C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C19C2×C3
LCSG ▷ C7×C11×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2926

Conjugacy classes & character table

1054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 92);