Finite Group Databasebeta

← Prev (#31798259) Next (#31798261) →

D7×C11⋊(D19⋊C3) #31798260

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

Aliases

direct productD7×C11⋊(D19⋊C3)
unambiguous semidirect product(D7×C19⋊C3)⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C22×C3
HallD7×D209 ⋊ C3
HallC7×C11×C19⋊C3 ⋊ C22
HallC11×C19⋊C3 ⋊ C2×D7
HallC7×C19⋊C3 ⋊ C2×D11
HallC11×C19 ⋊ C2×C3×D7
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ D7×D11
SylowC19 ⋊ C3×D7×D11
SylowC11 ⋊ D7×D19⋊C3
SylowC7 ⋊ C2×C11⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C19C22×C3
LCSG ▷ C7×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 75);