Finite Group Databasebeta

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C3×D7×#833 #72246815

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

Aliases

direct productC3×D7×#833

Splittings

HallC32×C7 ⋊ C2×#100
SylowC32 ⋊ D7×#100
SylowC7 ⋊ C2×C3×#833

Subgroups

subgroupG/H
centerC2×C3D7×#217
commutatorC22×C3×C7C22×C3×C4
FrattiniC2×C4C2×C3×D3×D7
FittingC2×C32×C7×D4C22
socleC2×C32×C7C2×C22⋊C4
prime radicalC2×C32×D4×D7C2
cosocleC2×C3×C4×C7C23×C3
hypercenterC2×C3×D4D3×D7
hypocenterC3×C7C2×C3×#100
LCSG ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

980 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD7×#10591503, C3×D7×#5077, D7×#10591510
maximal normal subgroup ofD7×#10591503, C3×D7×#5077, D7×#10591510

GAP

Past the SmallGroups library coverage — no SmallGroups id.