Finite Group DatabasebetaFinite Group Databasebeta| order | 19210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D565 |
| unambiguous semidirect product | C5⋊(C17×D113) |
| unambiguous semidirect product | C113⋊(D5×C17) |
| Fitting, socle, Hall | C5×C17×C113 ⋊ C2 |
| derived, Hall | C5×C113 ⋊ C2×C17 |
| Hall | C17×C113 ⋊ D5 |
| Sylow | C113 ⋊ D5×C17 |
| Hall | C5×C17 ⋊ D113 |
| Sylow | C5 ⋊ C17×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D565 |
| commutator, cosocle, hypocenter | C5×C113 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C113 | C2 |
| LCS | G ▷ C5×C113 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9605 |
4828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#14555933, C17×#14555934, #50307435, … |
| maximal normal subgroup of | C17×#14555933, C17×#14555934, #50307435, … |
| maximal quotient of | C17×Dic565, C2×C17×D565 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19210, 6);