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C2×C3×Dic3×AGL(1,𝔽7) #72246498

order3024
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3×Dic3×AGL(1,𝔽7)

Splittings

derivedC3×C7 ⋊ C22×C32×C4
HallC32×ΓL(1,𝔽8) ⋊ C22×C4
SylowC7 ⋊ C22×C32×Dic3

Subgroups

subgroupG/H
center, hypercenterC22×C3D3×AGL(1,𝔽7)
commutator, hypocenterC3×C7C22×C32×C4
FrattiniC2C2×C3×D3×AGL(1,𝔽7)
Fitting, socleC22×C32×C7C22×C3
prime radicalC22×C32×AGL(1,𝔽7)C2
cosocleC2×C3×C7C23×C32
LCSG ▷ C3×C7
UCSC1 ◁ C22×C3

904 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 ofC2×AGL(1,𝔽7)×#624, C2×C3×#67×AGL(1,𝔽7), C2×AGL(1,𝔽7)×#626, …
maximal normal subgroup ofC2×AGL(1,𝔽7)×#624, C2×C3×#67×AGL(1,𝔽7), C2×AGL(1,𝔽7)×#626, …
maximal quotient ofC3×AGL(1,𝔽7)×#208

GAP

Past the SmallGroups library coverage — no SmallGroups id.