Finite Group Databasebeta

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C19×D17×C11⋊C5 #48001054

order35530
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D17×C11⋊C5
unambiguous semidirect productC17⋊(C2×C19×C11⋊C5)
unambiguous semidirect product(C11×D17)⋊(C5×C19)
unambiguous semidirect product(C11×C19×D17)⋊C5

Splittings

Fitting, socle, HallC11×C17×C19 ⋊ C2×C5
derived, HallC11×C17 ⋊ C2×C5×C19
HallC17×C19×C11⋊C5 ⋊ C2
HallC11×C19×D17 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×C19
HallC11×D17 ⋊ C5×C19
HallC17×C19 ⋊ C2×C11⋊C5
HallC11×C19 ⋊ C5×D17
SylowC17 ⋊ C2×C19×C11⋊C5
SylowC11 ⋊ C5×C19×D17

Subgroups

subgroupG/H
center, hypercenterC19D17×C11⋊C5
commutator, cosocle, hypocenterC11×C17C2×C5×C19
FrattiniC1G
Fitting, socleC11×C17×C19C2×C5
LCSG ▷ C11×C17
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3553

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 19);