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C17×D19×C11⋊C5 #48001053

order35530
automorphism?
homologyAbelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D19×C11⋊C5
unambiguous semidirect productC19⋊(C2×C17×C11⋊C5)
unambiguous semidirect product(C11×D19)⋊(C5×C17)
unambiguous semidirect product(C11×C17×D19)⋊C5

Splittings

Fitting, socle, HallC11×C17×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C5×C17
HallC17×C19×C11⋊C5 ⋊ C2
HallC11×C17×D19 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C17
HallC11×D19 ⋊ C5×C17
HallC17×C19 ⋊ C2×C11⋊C5
HallC11×C17 ⋊ C5×D19
SylowC19 ⋊ C2×C17×C11⋊C5
SylowC11 ⋊ C5×C17×D19

Subgroups

subgroupG/H
center, hypercenterC17D19×C11⋊C5
commutator, cosocle, hypocenterC11×C19C2×C5×C17
FrattiniC1G
Fitting, socleC11×C17×C19C2×C5
LCSG ▷ C11×C19
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3553

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 18);