Finite Group DatabasebetaFinite Group Databasebeta| order | 17499 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C307⋊C3 |
| unambiguous semidirect product | C307⋊(C3×C19) |
| Fitting, socle, Hall | C19×C307 ⋊ C3 |
| derived, Sylow | C307 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C307⋊C3 |
| commutator, cosocle, hypocenter | C307 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C307 | C3 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5833 |
1995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×C307⋊C3, C19×D307⋊C3, D19×C307⋊C3, … |
| maximal normal subgroup of | C2×C19×C307⋊C3, C19×D307⋊C3, D19×C307⋊C3, … |
| maximal quotient of | C2×C19×C307⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17499, 2);