Finite Group DatabasebetaFinite Group Databasebeta| order | 17204 |
| isoclinism | isoclinic class of D187 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D187 |
| unambiguous semidirect product | (C2×C11)⋊(C23×D17) |
| unambiguous semidirect product | (C2×C17)⋊(D11×C23) |
| Fitting, socle | C2×C11×C17×C23 ⋊ C2 |
| derived, Hall | C11×C17 ⋊ C22×C23 |
| Hall | C11×C17×C23 ⋊ C22 |
| Hall | C17×C23 ⋊ C2×D11 |
| Hall | C11×C23 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D11×C23 |
| Sylow | C11 ⋊ C2×C23×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D187 |
| commutator, cosocle, hypocenter | C11×C17 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C17×C23 | C2 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C2×C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8602 |
4370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17204, 33);