Finite Group Databasebeta

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C11×D1615 #48001048

order35530
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1615
unambiguous semidirect productC5⋊(C11×D323)
unambiguous semidirect productC17⋊(C11×D95)
unambiguous semidirect productC19⋊(C11×D85)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, HallC5×C17×C19 ⋊ C2×C11
HallC11×C17×C19 ⋊ D5
HallC5×C11×C19 ⋊ D17
HallC5×C11×C17 ⋊ D19
HallC17×C19 ⋊ D5×C11
HallC11×C19 ⋊ D85
HallC11×C17 ⋊ D95
HallC5×C19 ⋊ C11×D17
HallC5×C17 ⋊ C11×D19
HallC5×C11 ⋊ D323
SylowC19 ⋊ C11×D85
SylowC17 ⋊ C11×D95
SylowC5 ⋊ C11×D323

Subgroups

subgroupG/H
center, hypercenterC11D1615
commutator, cosocle, hypocenterC5×C17×C19C2×C11
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C5×C17×C19
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17765

Conjugacy classes & character table

8899 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 13);