Finite Group Databasebeta

← Prev (#31798970) Next (#31798972) →

C3×C19⋊(D31⋊C5) #31798971

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19⋊(D31⋊C5)
unambiguous semidirect product(C3×D589)⋊C5

Splittings

Fitting, socle, HallC3×C19×C31 ⋊ C2×C5
derived, HallC19×C31 ⋊ C2×C3×C5
HallC3×C19×ΓL(1,𝔽32) ⋊ C2
HallC3×D589 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
HallD589 ⋊ C3×C5
HallC3×ΓL(1,𝔽32) ⋊ D19
HallΓL(1,𝔽32) ⋊ C3×D19
HallC3×C31 ⋊ C5×D19
HallC3×C19 ⋊ D31⋊C5
SylowC31 ⋊ C3×C5×D19
SylowC19 ⋊ C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C19⋊(D31⋊C5)
commutator, cosocle, hypocenterC19×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C19×C31C2×C5
LCSG ▷ C19×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1767

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D19×D31⋊C5, D3×C19⋊(D31⋊C5), D57⋊(D31⋊C5), …
maximal normal subgroup ofC3×D19×D31⋊C5, D3×C19⋊(D31⋊C5), D57⋊(D31⋊C5), …
maximal quotient ofC3×C19⋊(Dic31⋊C5), C2×C3×C19⋊(D31⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 28);