Finite Group Databasebeta

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C5×C11×D323 #48001040

order35530
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D323
unambiguous semidirect productC17⋊(C5×C11×D19)
unambiguous semidirect productC19⋊(C5×C11×D17)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, HallC17×C19 ⋊ C2×C5×C11
HallC11×C17×C19 ⋊ C2×C5
HallC5×C17×C19 ⋊ C2×C11
HallC5×C11×C19 ⋊ D17
HallC5×C11×C17 ⋊ D19
HallC11×C19 ⋊ C5×D17
HallC11×C17 ⋊ C5×D19
HallC5×C19 ⋊ C11×D17
HallC5×C17 ⋊ C11×D19
SylowC19 ⋊ C5×C11×D17
SylowC17 ⋊ C5×C11×D19

Subgroups

subgroupG/H
center, hypercenterC5×C11D323
commutator, cosocle, hypocenterC17×C19C2×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C17×C19
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17765

Conjugacy classes & character table

8965 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 5);