Finite Group Databasebeta

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C5×C29⋊(D19⋊C3) #30658359

order16530
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29⋊(D19⋊C3)
unambiguous semidirect productC29⋊(C5×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C5×D29)
unambiguous semidirect productD551⋊(C3×C5)
unambiguous semidirect product(C5×D551)⋊C3

Splittings

Fitting, socle, HallC5×C19×C29 ⋊ C2×C3
derived, HallC19×C29 ⋊ C2×C3×C5
HallC5×C29×C19⋊C3 ⋊ C2
HallC5×D551 ⋊ C3
HallC29×C19⋊C3 ⋊ C2×C5
HallD551 ⋊ C3×C5
HallC5×C19⋊C3 ⋊ D29
HallC5×C29 ⋊ D19⋊C3
HallC5×C19 ⋊ C3×D29
HallC19⋊C3 ⋊ C5×D29
SylowC29 ⋊ C5×D19⋊C3
SylowC19 ⋊ C3×C5×D29

Subgroups

subgroupG/H
center, hypercenterC5C29⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C29C2×C3×C5
FrattiniC1G
Fitting, socleC5×C19×C29C2×C3
LCSG ▷ C19×C29
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2755

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D29×D19⋊C3, D5×C29⋊(D19⋊C3), D145⋊(D19⋊C3), …
maximal normal subgroup ofC5×D29×D19⋊C3, D5×C29⋊(D19⋊C3), D145⋊(D19⋊C3), …
maximal quotient ofC5×(C19⋊C3)⋊Dic29, C2×C5×C29⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16530, 20);