Finite Group Databasebeta

← Prev (#30633461) Next (#30633463) →

C3×C5×D539 #30633462

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D539

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC11×C49 ⋊ C2×C3×C5
HallC5×C11×C49 ⋊ C2×C3
HallC3×C11×C49 ⋊ C2×C5
HallC3×C5×C49 ⋊ D11
HallC5×C49 ⋊ C3×D11
HallC3×C5×C11 ⋊ D49
HallC3×C49 ⋊ C5×D11
HallC5×C11 ⋊ C3×D49
SylowC49 ⋊ C3×C5×D11
HallC3×C11 ⋊ C5×D49
SylowC11 ⋊ C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC3×C5D539
commutator, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7C3×C5×D77
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11D7
LCSG ▷ C11×C49
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4065 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D11×D49, C3×D5×D539, C3×D55⋊D49, …
maximal normal subgroup ofC3×C5×D11×D49, C3×D5×D539, C3×D55⋊D49, …
maximal quotient ofC3×C5×Dic539, C2×C3×C5×D539

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 7);