Finite Group Databasebeta

← Prev (#34035208) Next (#34035210) →

C22×C5×C17×C11⋊C5 #34035209

order18700
automorphism?
homologyAbelianization (H1) = C22×C52×C17 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C5×C17×C11⋊C5
unambiguous semidirect product(C22×C11)⋊(C52×C17)
unambiguous semidirect product(C22×C5×C11)⋊(C5×C17)
unambiguous semidirect product(C22×C11×C17)⋊C52
unambiguous semidirect product(C22×C5×C11×C17)⋊C5

Splittings

Fitting, socleC22×C5×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C22×C52×C17
HallC22×C11×C17 ⋊ C52
HallC11×C17 ⋊ C22×C52
HallC22×C11 ⋊ C52×C17

Subgroups

subgroupG/H
center, hypercenterC22×C5×C17C11⋊C5
commutator, cosocle, hypocenterC11C22×C52×C17
FrattiniC1G
Fitting, socleC22×C5×C11×C17C5
LCSG ▷ C11
UCSC1 ◁ C22×C5×C17

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3740

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 94);