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C29×C5⋊(D19⋊C3) #30658362

order16530
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C5⋊(D19⋊C3)
unambiguous semidirect productC5⋊(C29×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D5×C29)
unambiguous semidirect productD95⋊(C3×C29)
unambiguous semidirect product(C29×D95)⋊C3

Splittings

Fitting, socle, HallC5×C19×C29 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C3×C29
HallC5×C29×C19⋊C3 ⋊ C2
HallC29×D95 ⋊ C3
HallC29×C19⋊C3 ⋊ D5
HallC19×C29 ⋊ C3×D5
HallC5×C19⋊C3 ⋊ C2×C29
HallD95 ⋊ C3×C29
HallC5×C29 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D5×C29
SylowC19 ⋊ C3×D5×C29
SylowC5 ⋊ C29×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC29C5⋊(D19⋊C3)
commutator, cosocle, hypocenterC5×C19C2×C3×C29
FrattiniC1G
Fitting, socleC5×C19×C29C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2755

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD29×C5⋊(D19⋊C3), D5×C29×D19⋊C3, D145⋊(D19⋊C3), …
maximal normal subgroup ofD29×C5⋊(D19⋊C3), D5×C29×D19⋊C3, D145⋊(D19⋊C3), …
maximal quotient ofC29×(C19⋊C3)⋊Dic5, C2×C29×C5⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16530, 23);