Finite Group Databasebeta

← Prev (#34087281) Next (#34087283) →

C3×C7×C17×C11⋊C5 #34087282

order19635
automorphism?
homologyAbelianization (H1) = C3×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C17×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C7×C17)
unambiguous semidirect product(C3×C11)⋊(C5×C7×C17)
unambiguous semidirect product(C11×C17)⋊(C3×C5×C7)
unambiguous semidirect product(C3×C7×C11)⋊(C5×C17)
unambiguous semidirect product(C3×C11×C17)⋊(C5×C7)
unambiguous semidirect product(C3×C7×C11×C17)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C7×C17
HallC7×C11×C17 ⋊ C3×C5
HallC3×C11×C17 ⋊ C5×C7
HallC3×C7×C11 ⋊ C5×C17
HallC11×C17 ⋊ C3×C5×C7
HallC7×C11 ⋊ C3×C5×C17
HallC3×C11 ⋊ C5×C7×C17

Subgroups

subgroupG/H
center, hypercenterC3×C7×C17C11⋊C5
commutator, cosocle, hypocenterC11C3×C5×C7×C17
FrattiniC1G
Fitting, socleC3×C7×C11×C17C5
LCSG ▷ C11
UCSC1 ◁ C3×C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

2499 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19635, 2);