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C5×D1617 #30633470

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

Aliases

direct productC5×D1617
unambiguous semidirect productC3⋊(C5×D539)
unambiguous semidirect productC49⋊(C5×D33)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC3×C11×C49 ⋊ C2×C5
HallC5×C11×C49 ⋊ D3
HallC3×C5×C49 ⋊ D11
HallC11×C49 ⋊ C5×D3
HallC5×C49 ⋊ D33
HallC3×C5×C11 ⋊ D49
HallC3×C49 ⋊ C5×D11
HallC5×C11 ⋊ D147
SylowC49 ⋊ C5×D33
HallC3×C11 ⋊ C5×D49
HallC3×C5 ⋊ D539
SylowC11 ⋊ C5×D147
SylowC3 ⋊ C5×D539

Subgroups

subgroupG/H
center, hypercenterC5D1617
commutator, cosocle, hypocenterC3×C11×C49C2×C5
FrattiniC7C5×D231
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11D7
LCSG ▷ C3×C11×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×D147, C5×D33×D49, C5×D3×D539, …
maximal normal subgroup ofC5×D11×D147, C5×D33×D49, C5×D3×D539, …
maximal quotient ofC5×Dic1617, C2×C5×D1617

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 15);