Finite Group Databasebeta

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D3×C23×D19⋊C3 #30628604

order15732
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productD3×C23×D19⋊C3
unambiguous semidirect productD19⋊(C3×D3×C23)
unambiguous semidirect product(D3×D19)⋊(C3×C23)
unambiguous semidirect product(C3×D19⋊C3)⋊(C2×C23)
unambiguous semidirect product(D3×C19⋊C3)⋊(C2×C23)
unambiguous semidirect product(C3⋊(D19⋊C3))⋊(C2×C23)
unambiguous semidirect product(D3×C23×D19)⋊C3

Splittings

Fitting, socleC3×C19×C23 ⋊ C22×C3
derivedC3×C19 ⋊ C22×C3×C23
HallC3×C23×C19⋊C3 ⋊ C22
HallC19×C23 ⋊ C2×C3×D3
HallC3×C19⋊C3 ⋊ C22×C23
SylowC19 ⋊ C2×C3×D3×C23

Subgroups

subgroupG/H
center, hypercenterC23D3×D19⋊C3
commutator, cosocle, hypocenterC3×C19C22×C3×C23
FrattiniC1G
Fitting, socleC3×C19×C23C22×C3
LCSG ▷ C3×C19
UCSC1 ◁ C23

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1311

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 66);