Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| isoclinism | isoclinic class of C5⋊D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C19×C5⋊D45 |
| unambiguous semidirect product | (C2×C5)⋊(C19×D45) |
| unambiguous semidirect product | (C2×C9)⋊(C19×C5⋊D5) |
| Fitting | C2×C52×C9×C19 ⋊ C2 |
| derived, Hall | C52×C9 ⋊ C22×C19 |
| Hall | C52×C9×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D9 |
| Hall | C9×C19 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D9×C19 |
| Sylow | C9 ⋊ C2×C19×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | C5⋊D45 |
| commutator, cosocle, hypocenter | C52×C9 | C22×C19 |
| Frattini | C3 | C2×C19×C3⋊(C5⋊D5) |
| Fitting | C2×C52×C9×C19 | C2 |
| socle | C2×C3×C52×C19 | D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C2×C19 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8550 |
4332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 264);