Finite Group Databasebeta

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C4×D9×AGL(1,𝔽7) #72277913

order3024
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D9×AGL(1,𝔽7)

Splittings

FittingC4×C7×C9 ⋊ C22×C3
derivedC7×C9 ⋊ C22×C3×C4
HallC9×ΓL(1,𝔽8) ⋊ C22×C4
SylowC7 ⋊ C2×C3×C4×D9

Subgroups

subgroupG/H
center, hypercenterC4D9×AGL(1,𝔽7)
commutator, hypocenterC7×C9C22×C3×C4
FrattiniC2×C3C2×D3×AGL(1,𝔽7)
FittingC4×C7×C9C22×C3
socleC2×C3×C7C22×C3×D3
prime radicalC2×D9×AGL(1,𝔽7)C2
cosocleC2×C7×C9C23×C3
LCSG ▷ C7×C9
UCSC1 ◁ C4

356 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 252

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.