Finite Group Databasebeta

← Prev (#34035195) Next (#34035197) →

D5×C17×AGL(1,𝔽11) #34035196

order18700
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productD5×C17×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D5×C17)
unambiguous semidirect product(D5×D11)⋊(C5×C17)
unambiguous semidirect product(C5×AGL(1,𝔽11))⋊(C2×C17)
unambiguous semidirect product(D5×C11⋊C5)⋊(C2×C17)
unambiguous semidirect product(C5⋊AGL(1,𝔽11))⋊(C2×C17)
unambiguous semidirect product(D5×C17×D11)⋊C5

Splittings

Fitting, socleC5×C11×C17 ⋊ C22×C5
derivedC5×C11 ⋊ C22×C5×C17
HallC5×C17×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C17
HallC11×C17 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C5×D5×C17

Subgroups

subgroupG/H
center, hypercenterC17D5×AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C22×C5×C17
FrattiniC1G
Fitting, socleC5×C11×C17C22×C5
LCSG ▷ C5×C11
UCSC1 ◁ C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 935

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 81);