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C2×D3×D4×AGL(1,𝔽5) #14478832

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D3×D4×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C4×D3×D4)
unambiguous semidirect product(D3×D5)⋊(C4×D4)

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C22×C4×D4
SylowC5 ⋊ C2×C4×D3×D4
SylowC3 ⋊ C22×D4×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D3×D4×D5C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C22×C4×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

5056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#120, D3×AGL(1,𝔽5)×H(5,𝔽2), D3×AGL(1,𝔽5)×#99, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×#120, D3×AGL(1,𝔽5)×H(5,𝔽2), D3×AGL(1,𝔽5)×#99, …
maximal quotient ofD3×AGL(1,𝔽5)×#120, D3×AGL(1,𝔽5)×#127, D3×AGL(1,𝔽5)×AGL(1,ℤ/8), …
automorphism group of#6652, #6653, #6654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204530);