Finite Group DatabasebetaFinite Group Databasebeta| order | 17630 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1763 |
| unambiguous semidirect product | C43⋊(C5×D41) |
| Fitting, socle, Hall | C5×C41×C43 ⋊ C2 |
| derived, Hall | C41×C43 ⋊ C2×C5 |
| Hall | C5×C43 ⋊ D41 |
| Hall | C5×C41 ⋊ D43 |
| Sylow | C43 ⋊ C5×D41 |
| Sylow | C41 ⋊ C5×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1763 |
| commutator, cosocle, hypocenter | C41×C43 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C41×C43 | C2 |
| LCS | G ▷ C41×C43 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8815 |
4415 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D41×D43, D5×D1763, D205⋊D43, … |
| maximal normal subgroup of | C5×D41×D43, D5×D1763, D205⋊D43, … |
| maximal quotient of | C5×Dic1763, C2×C5×D1763 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17630, 5);