Finite Group DatabasebetaFinite Group Databasebeta| order | 21012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C103⋊C17 |
| unambiguous semidirect product | C3⋊(C4×C103⋊C17) |
| unambiguous semidirect product | (Dic3×C103)⋊C17 |
| derived, Hall | C3×C103 ⋊ C4×C17 |
| Hall | C3×C103⋊C17 ⋊ C4 |
| Hall | Dic3×C103 ⋊ C17 |
| Sylow | C103 ⋊ Dic3×C17 |
| Sylow | C3 ⋊ C4×C103⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C103⋊C17 |
| commutator, hypocenter | C3×C103 | C4×C17 |
| Fitting, socle, cosocle | C2×C3×C103 | C2×C17 |
| prime radical | C2×C3×C103⋊C17 | C2 |
| LCS | G ▷ C3×C103 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1236 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21012, 13);