Finite Group DatabasebetaFinite Group Databasebeta| order | 17790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2965 |
| unambiguous semidirect product | C5⋊(C3×D593) |
| unambiguous semidirect product | C593⋊(C3×D5) |
| Fitting, socle, Hall | C3×C5×C593 ⋊ C2 |
| derived, Hall | C5×C593 ⋊ C2×C3 |
| Hall | C3×C593 ⋊ D5 |
| Sylow | C593 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ D593 |
| Sylow | C5 ⋊ C3×D593 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2965 |
| commutator, cosocle, hypocenter | C5×C593 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C593 | C2 |
| LCS | G ▷ C5×C593 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8895 |
4452 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#26045083, C3×#26045084, C3×D5×D593, … |
| maximal normal subgroup of | C3×#26045083, C3×#26045084, C3×D5×D593, … |
| maximal quotient of | C3×Dic2965, C2×C3×D2965 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17790, 4);