Finite Group DatabasebetaFinite Group Databasebeta| order | 17204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D187 |
| unambiguous semidirect product | (C11×D23)⋊D17 |
| unambiguous semidirect product | (C17×D23)⋊D11 |
| Fitting, socle, derived, Hall | C11×C17×C23 ⋊ C22 |
| Hall | C17×C23 ⋊ C2×D11 |
| Hall | C11×C23 ⋊ C2×D17 |
| Hall | C11×C17 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D187 |
| Sylow | C17 ⋊ D11×D23 |
| Sylow | C11 ⋊ D17×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C17×C23 | C22 |
| LCS | G ▷ C11×C17×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4301 |
1235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17204, 27);