Finite Group Databasebeta

← Prev (#72245639) Next (#72245641) →

C2×D4×C3⋊(C3⋊AGL(1,𝔽7)) #72245640

order6048
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×D4×C3⋊(C3⋊AGL(1,𝔽7))

Splittings

FittingC2×C32×C7×D4 ⋊ C2×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×D4
SylowC7 ⋊ C2×C3×D4×C3⋊D3

Subgroups

subgroupG/H
centerC22C22×C3⋊(C3⋊AGL(1,𝔽7))
commutator, cosocleC2×C32×C7C24×C3
FrattiniC2C23×C3⋊(C3⋊AGL(1,𝔽7))
FittingC2×C32×C7×D4C2×C3
socleC22×C32×C7C23×C3
hypercenterC2×D4C3⋊(C3⋊AGL(1,𝔽7))
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C2×D4

3264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D4×C3⋊D3×AGL(1,𝔽7), #127×C3⋊(C3⋊AGL(1,𝔽7)), #72246558, …
maximal normal subgroup ofC2×D4×C3⋊D3×AGL(1,𝔽7), #127×C3⋊(C3⋊AGL(1,𝔽7)), #72246558, …
maximal quotient of#127×C3⋊(C3⋊AGL(1,𝔽7)), #120×C3⋊(C3⋊AGL(1,𝔽7))

GAP

Past the SmallGroups library coverage — no SmallGroups id.