Finite Group DatabasebetaFinite Group Databasebeta| order | 17204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C17×C23 ⋊ C22×C11 |
| Hall | C17×C23⋊C11 ⋊ C22 |
| Hall | D17×D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×D17 |
| Sylow | C23 ⋊ C2×C11×D17 |
| Sylow | C17 ⋊ C2×AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C23 | C22×C11 |
| LCS | G ▷ C17×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 391 |
230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17204, 16);