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D3×#64862 #14294472

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD3×#64862

Splittings

FittingC3×C42×C5 ⋊ C2×C4
HallC3×C5 ⋊ C2×#339
SylowC5 ⋊ D3×#339
SylowC3 ⋊ C2×#64862

Subgroups

subgroupG/H
centerC4D3×C4⋊AGL(1,𝔽5)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC2×C3×C5C2×#95
prime radicalC22×D3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#339
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#104, D3×#10604003, D3×#10604614, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×#104, D3×#10604003, D3×#10604614
maximal quotient of#72260242

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20170);