Finite Group Databasebeta

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C3×#67⋊ΓL(1,𝔽16) #72269760

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

Aliases

direct productC3×#67⋊ΓL(1,𝔽16)

Splittings

FittingC22×C33×C5 ⋊ C2×C4
HallC33×C5 ⋊ C4×D4
SylowC33 ⋊ D4×AGL(1,𝔽5)
SylowC5 ⋊ C3×#67⋊Dic3

Subgroups

subgroupG/H
centerC2×C3C2×D3×ΓL(1,𝔽16)
commutatorC2×C32×C5C22×C3×C4
FrattiniC2C2×C3×D3×ΓL(1,𝔽16)
FittingC22×C33×C5C2×C4
socleC2×C33×C5C22×C4
prime radicalC32×D5×#67C2
cosocleC2×C32×D5C23×C3
hypercenterC22×C3D3×ΓL(1,𝔽16)
hypocenterC32×C5C3×C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2×C3 ◁ C22×C3

1100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#3811
maximal normal subgroup ofC3×AGL(1,𝔽5)×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.