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D3×D5×3−1+2 #13108398

order1620
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2

Aliases

direct productD3×D5×3−1+2
unambiguous semidirect product(C5×D3)⋊(C2×3−1+2)
unambiguous semidirect product(C3×D5)⋊(C2×3−1+2)
unambiguous semidirect productD15⋊(C2×3−1+2)
unambiguous semidirect product(D3×C9×D5)⋊C3

Splittings

Fitting, HallC3×C5×3−1+2 ⋊ C22
SylowC3×3−1+2 ⋊ C2×D5
SylowC5 ⋊ C2×D3×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×D3×D5
commutator, socle, cosocleC32×C5C22×C32
FittingC3×C5×3−1+2C22
prime radicalC32×D3×D5C3
hypercenter3−1+2D3×D5
hypocenterC3×C5C22×3−1+2
LCSG ▷ C32×C5 ▷ C3×C5
UCSC1 ◁ C3 ◁ 3−1+2

204 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#92265, D3×D5×AGL(1,ℤ/9), D3×AGL(1,𝔽5)×3−1+2, …
maximal normal subgroup ofD3×D5×AGL(1,ℤ/9), D3×AGL(1,𝔽5)×3−1+2, D3×3−1+2⋊AGL(1,𝔽5)
maximal quotient ofD5×#92265, D5×#92259, D5×S4×3−1+2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 304);