Finite Group Databasebeta

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C2×C4×C3⋊D3×AGL(1,𝔽7) #72245500

order6048
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×C4×C3⋊D3×AGL(1,𝔽7)

Splittings

FittingC2×C32×C4×C7 ⋊ C22×C3
derivedC32×C7 ⋊ C23×C3×C4
HallC32×ΓL(1,𝔽8) ⋊ C23×C4
SylowC7 ⋊ C22×C3×C4×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊D3×AGL(1,𝔽7)
commutator, hypocenterC32×C7C23×C3×C4
FrattiniC2C22×C3⋊D3×AGL(1,𝔽7)
FittingC2×C32×C4×C7C22×C3
socleC22×C32×C7C23×C3
prime radicalC22×C3⋊D3×AGL(1,𝔽7)C2
cosocleC2×C32×C7C24×C3
LCSG ▷ C32×C7
UCSC1 ◁ C2×C4

3264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D4×C3⋊D3×AGL(1,𝔽7), C42×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64306, …
maximal normal subgroup ofC2×D4×C3⋊D3×AGL(1,𝔽7), C42×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64306, …
maximal quotient ofC42×C3⋊D3×AGL(1,𝔽7), C22⋊C4×C3⋊D3×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.