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C5×D1653 #30658352

order16530
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1653
unambiguous semidirect productC3⋊(C5×D551)
unambiguous semidirect productC19⋊(C5×D87)
unambiguous semidirect productC29⋊(C5×D57)

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C2
derived, HallC3×C19×C29 ⋊ C2×C5
HallC5×C19×C29 ⋊ D3
HallC19×C29 ⋊ C5×D3
HallC3×C5×C29 ⋊ D19
HallC3×C5×C19 ⋊ D29
HallC5×C29 ⋊ D57
HallC5×C19 ⋊ D87
HallC3×C29 ⋊ C5×D19
HallC3×C19 ⋊ C5×D29
SylowC29 ⋊ C5×D57
SylowC19 ⋊ C5×D87
HallC3×C5 ⋊ D551
SylowC3 ⋊ C5×D551

Subgroups

subgroupG/H
center, hypercenterC5D1653
commutator, cosocle, hypocenterC3×C19×C29C2×C5
FrattiniC1G
Fitting, socleC3×C5×C19×C29C2
LCSG ▷ C3×C19×C29
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

4140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D29×D57, C5×D19×D87, C5×D3×D551, …
maximal normal subgroup ofC5×D29×D57, C5×D19×D87, C5×D3×D551, …
maximal quotient ofC5×Dic1653, C2×C5×D1653

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16530, 13);