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C29×D285 #30658355

order16530
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D285
unambiguous semidirect productC3⋊(C29×D95)
unambiguous semidirect productC5⋊(C29×D57)
unambiguous semidirect productC19⋊(C29×D15)

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C2
derived, HallC3×C5×C19 ⋊ C2×C29
HallC5×C19×C29 ⋊ D3
HallC3×C19×C29 ⋊ D5
HallC19×C29 ⋊ D15
HallC3×C5×C29 ⋊ D19
HallC5×C29 ⋊ D57
HallC5×C19 ⋊ D3×C29
HallC3×C29 ⋊ D95
HallC3×C19 ⋊ D5×C29
SylowC19 ⋊ C29×D15
HallC3×C5 ⋊ C29×D19
SylowC5 ⋊ C29×D57
SylowC3 ⋊ C29×D95

Subgroups

subgroupG/H
center, hypercenterC29D285
commutator, cosocle, hypocenterC3×C5×C19C2×C29
FrattiniC1G
Fitting, socleC3×C5×C19×C29C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

4176 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD29×D285, C29×D15×D19, D551⋊D15, …
maximal normal subgroup ofD29×D285, C29×D15×D19, D551⋊D15, …
maximal quotient ofC29×Dic285, C2×C29×D285

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16530, 16);