Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊(#6923⋊C3) |
| unambiguous semidirect product | C3⋊(C5×#6923⋊C3) |
| unambiguous semidirect product | (C5×C3⋊#6923)⋊C3 |
| Fitting, socle | C3×C5×C61 ⋊ C3×C4 |
| derived | C3×C61 ⋊ C3×C4×C5 |
| Hall | C3×C5×C61⋊C3 ⋊ C4 |
| Hall | C3×C61⋊C3 ⋊ C4×C5 |
| Hall | C5×C61 ⋊ C3×Dic3 |
| Sylow | C61 ⋊ C3×C5×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(#6923⋊C3) |
| commutator, hypocenter | C3×C61 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C61 | C3×C4 |
| prime radical | C3×C5×D61⋊C3 | C2 |
| cosocle | C3×D61 | C2×C3×C5 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C5 | |
56 conjugacy classes of subgroups.
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 130);