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C3×C3⋊C8×AGL(1,𝔽7) #72254131

order3024
automorphism?
homologyAbelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C3⋊C8×AGL(1,𝔽7)

Splittings

derivedC3×C7 ⋊ C2×C32×C8
HallC32×ΓL(1,𝔽8) ⋊ C2×C8
SylowC7 ⋊ C2×C32×C3⋊C8

Subgroups

subgroupG/H
center, hypercenterC3×C4D3×AGL(1,𝔽7)
commutator, hypocenterC3×C7C2×C32×C8
FrattiniC4C3×D3×AGL(1,𝔽7)
FittingC32×C4×C7C22×C3
socleC2×C32×C7C2×C3×C4
prime radicalC2×C32×AGL(1,𝔽7)C4
cosocleC3×C4×C7C22×C32
LCSG ▷ C3×C7
UCSC1 ◁ C3×C4

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#3710, C3×AGL(1,𝔽7)×#208, AGL(1,𝔽7)×#3712, …
maximal normal subgroup ofAGL(1,𝔽7)×#3710, C3×AGL(1,𝔽7)×#208, AGL(1,𝔽7)×#3712, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.