Finite Group Databasebeta

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C3×C7×#5077 #72246832

order4032
automorphism?
homologyAbelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C23

Aliases

direct productC3×C7×#5077

Splittings

FittingC32×C7×#127 ⋊ C2
HallC32×C7 ⋊ #453
SylowC32 ⋊ C7×#453

Subgroups

subgroupG/H
centerC2×C3×C7#937
commutator, cosocleC2×C3×C4C23×C3×C7
FrattiniC2×C4C22×C3×D3×C7
FittingC32×C7×#127C2
socleC2×C32×C7#120
hypercenterC3×C7×#127D3
hypocenterC3C3×C7×#453
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C7 ◁ C2×C3×C4×C7 ◁ C3×C7×#127

780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×#11864777, C3×D7×#5077, #72247048
maximal normal subgroup ofC7×#11864777, C3×D7×#5077, #72247048

GAP

Past the SmallGroups library coverage — no SmallGroups id.