Finite Group Databasebeta

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C3×D7×#237 #72246573

order2016
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×D7×#237

Splittings

FittingC32×C7×D4 ⋊ C22
HallC32×C7 ⋊ C2×#41
SylowC32 ⋊ D7×#41
SylowC7 ⋊ C2×C3×#237

Subgroups

subgroupG/H
centerC2×C3C22×D3×D7
commutator, cosocleC2×C3×C7C24×C3
FrattiniC2C22×C3×D3×D7
FittingC32×C7×D4C22
socleC2×C32×C7C24
hypercenterC3×D4D3×D7
hypocenterC3×C7C2×C3×#41
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C3 ◁ C3×D4

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×#64312, C3×D7×#1004, D7×#64314, …
maximal normal subgroup ofD7×#64312, C3×D7×#1004, D7×#64314, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.