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D3×#65699 #14320267

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×#65699

Splittings

FittingC3×C5×C22⋊C4 ⋊ C2×C4
HallC3×C5 ⋊ C2×#385
SylowC5 ⋊ D3×#385
SylowC3 ⋊ C2×#65699

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC23×D3×D5C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#385
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

2464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#120, D3×#10603919, C3⋊D3×#65699
maximal normal subgroup ofD3×AGL(1,𝔽5)×#120, D3×#10603919
maximal quotient ofD3×#10603919, D3×#10604003, D3×#10603925, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45965);