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D3×#41×AGL(1,𝔽5) #14478943

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#41×AGL(1,𝔽5)

Splittings

FittingC3×C5×#41 ⋊ C2×C4
HallC3×C5 ⋊ C2×C4×#41
SylowC5 ⋊ C4×D3×#41
SylowC3 ⋊ C2×#41×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC4C22×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC3×C5×#41C2×C4
prime radicalD3×D5×#41C2
cosocleC2×C3×D5C25
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ #41

3456 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)×H(5,𝔽2), D3×AGL(1,𝔽5)×AGL(1,ℤ/8), D3×AGL(1,𝔽5)×#104, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), D3×AGL(1,𝔽5)×AGL(1,ℤ/8), D3×AGL(1,𝔽5)×#104
maximal quotient ofAGL(1,𝔽5)×#64306, D3×#13107559, AGL(1,𝔽5)×#64312, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204641);