Finite Group DatabasebetaFinite Group Databasebeta| order | 17430 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C7×D83 |
| unambiguous semidirect product | C83⋊(C2×C3×C5×C7) |
| Fitting, socle, Hall | C3×C5×C7×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C3×C5×C7 |
| Hall | C5×C7×C83 ⋊ C2×C3 |
| Hall | C3×C7×C83 ⋊ C2×C5 |
| Hall | C3×C5×C83 ⋊ C2×C7 |
| Hall | C7×C83 ⋊ C2×C3×C5 |
| Hall | C5×C83 ⋊ C2×C3×C7 |
| Hall | C3×C83 ⋊ C2×C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C7 | D83 |
| commutator, cosocle, hypocenter | C83 | C2×C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C3×C5×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8715 |
4515 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D7×D83, C3×C7×D5×D83, C3×D35×D83, … |
| maximal normal subgroup of | C3×C5×D7×D83, C3×C7×D5×D83, C3×D35×D83, … |
| maximal quotient of | C3×C5×C7×Dic83, C2×C3×C5×C7×D83 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17430, 3);