Finite Group Databasebeta

← Prev (#31798282) Next (#31798284) →

C2×C11⋊#11716322 #31798283

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

Aliases

direct productC2×C11⋊#11716322
unambiguous semidirect product(C2×C11)⋊#11716322

Splittings

Fitting, socleC2×C7×C11×C19 ⋊ C2×C3
derived, HallC7×C11×C19 ⋊ C22×C3
HallC2×C7×D209 ⋊ C3
HallC11×#87705 ⋊ C22
HallC2×D209 ⋊ ΓL(1,𝔽8)
Hall#87705 ⋊ C2×D11
HallC11×C19 ⋊ C22×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D19⋊C3
SylowC19 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×#11716322
SylowC7 ⋊ C2×C11⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C11⋊#11716322
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 98);