Finite Group Databasebeta

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C4×ΓL(1,𝔽8)×AGL(1,𝔽9) #72217372

order6048
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productC4×ΓL(1,𝔽8)×AGL(1,𝔽9)

Splittings

FittingC32×C4×C7 ⋊ C3×C8
derivedC32×C7 ⋊ C3×C4×C8
HallC32×ΓL(1,𝔽8) ⋊ C4×C8
SylowC7 ⋊ C3×C4×AGL(1,𝔽9)

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×AGL(1,𝔽9)
commutator, hypocenterC32×C7C3×C4×C8
FrattiniC2C2×ΓL(1,𝔽8)×AGL(1,𝔽9)
FittingC32×C4×C7C3×C8
socleC2×C32×C7C2×C3×C8
prime radicalC2×C3⋊D3×ΓL(1,𝔽8)C2×C4
cosocleC2×C7×#157C22×C3
LCSG ▷ C32×C7
UCSC1 ◁ C4

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×AGL(1,𝔽9), C4×AGL(1,𝔽7)×AGL(1,𝔽9)
maximal normal subgroup ofC4×AGL(1,𝔽7)×AGL(1,𝔽9)
maximal quotient ofAGL(1,𝔽5)×ΓL(1,𝔽8)×AGL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.