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D4×3−1+2⋊AGL(1,𝔽5) #72247442

order4320
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productD4×3−1+2⋊AGL(1,𝔽5)

Splittings

FittingC5×D4×3−1+2 ⋊ C4
HallC5×3−1+2 ⋊ C4×D4
Sylow3−1+2 ⋊ D4×AGL(1,𝔽5)
SylowC5 ⋊ D4×3−1+2⋊C4

Subgroups

subgroupG/H
centerC2C22×3−1+2⋊AGL(1,𝔽5)
commutatorC2×C5×C9C22×C3×C4
FrattiniC2×C3C22×C3×ΓL(1,𝔽16)
FittingC5×D4×3−1+2C4
socleC2×C3×C5C22×C3×Dic3
prime radicalC32×D4×D5D3
cosocleC2×C9×D5C23×C3
hypercenterD43−1+2⋊AGL(1,𝔽5)
hypocenterC5×C9C3×C4×D4
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ D4

618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

155 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9), #72254787, S4×3−1+2⋊AGL(1,𝔽5)
maximal normal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9)
maximal quotient of#72254787

GAP

Past the SmallGroups library coverage — no SmallGroups id.