Finite Group Databasebeta

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C4×C3⋊Dic3×AGL(1,𝔽7) #72246431

order6048
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C3×C4

Aliases

direct productC4×C3⋊Dic3×AGL(1,𝔽7)

Splittings

derivedC32×C7 ⋊ C2×C3×C42
HallC32×ΓL(1,𝔽8) ⋊ C2×C42
SylowC7 ⋊ C2×C3×C4×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊D3×AGL(1,𝔽7)
commutator, hypocenterC32×C7C2×C3×C42
FrattiniC22C2×C3⋊D3×AGL(1,𝔽7)
FittingC2×C32×C4×C7C22×C3
socle, cosocleC22×C32×C7C23×C3
prime radicalC22×C32×AGL(1,𝔽7)C22
LCSG ▷ C32×C7
UCSC1 ◁ C2×C4

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1008

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC42×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64149
maximal normal subgroup ofC42×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64149

GAP

Past the SmallGroups library coverage — no SmallGroups id.