Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C3×C211 ⋊ C22×C7 |
| Hall | C3×C211⋊C7 ⋊ C22 |
| Hall | D3×D211 ⋊ C7 |
| Hall | C211⋊C7 ⋊ C2×D3 |
| Sylow | C211 ⋊ C2×D3×C7 |
| Sylow | C3 ⋊ C2×D211⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C211 | C22×C7 |
| LCS | G ▷ C3×C211 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 633 |
87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 33);