Finite Group Databasebeta

← Prev (#72254341) Next (#72254343) →

#104×C3⋊AGL(1,𝔽7) #72254342

order4032
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct product#104×C3⋊AGL(1,𝔽7)

Splittings

FittingC3×C7×#104 ⋊ C2×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#104
SylowC7 ⋊ C3×D3×#104

Subgroups

subgroupG/H
centerC4D4×C3⋊AGL(1,𝔽7)
commutatorC3×C4×C7C22×C3×C4
FrattiniC2×C4C22×C3⋊AGL(1,𝔽7)
FittingC3×C7×#104C2×C3
socleC2×C3×C7C2×C3×C22⋊C4
prime radical#41×C3⋊AGL(1,𝔽7)C2
cosocleC2×C3×C4×C7C23×C3
hypercenter#104C3⋊AGL(1,𝔽7)
hypocenterC3×C7C2×C3×#104
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#104×AGL(1,𝔽7), #453×C3⋊AGL(1,𝔽7), #72269426
maximal normal subgroup ofD3×#104×AGL(1,𝔽7), #453×C3⋊AGL(1,𝔽7), #72269426

GAP

Past the SmallGroups library coverage — no SmallGroups id.