Finite Group DatabasebetaFinite Group Databasebeta| order | 18802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1343 |
| unambiguous semidirect product | C17⋊(C7×D79) |
| unambiguous semidirect product | C79⋊(C7×D17) |
| Fitting, socle, Hall | C7×C17×C79 ⋊ C2 |
| derived, Hall | C17×C79 ⋊ C2×C7 |
| Hall | C7×C79 ⋊ D17 |
| Hall | C7×C17 ⋊ D79 |
| Sylow | C79 ⋊ C7×D17 |
| Sylow | C17 ⋊ C7×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1343 |
| commutator, cosocle, hypocenter | C17×C79 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C79 | C2 |
| LCS | G ▷ C17×C79 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9401 |
4711 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D17×D79, D7×D1343, D119⋊D79, … |
| maximal normal subgroup of | C7×D17×D79, D7×D1343, D119⋊D79, … |
| maximal quotient of | C7×Dic1343, C2×C7×D1343 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18802, 4);