Finite Group DatabasebetaFinite Group Databasebeta| order | 21522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D211⋊C3 |
| unambiguous semidirect product | D211⋊(C3×C17) |
| unambiguous semidirect product | (C211⋊C3)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D211)⋊C3 |
| Fitting, socle, Hall | C17×C211 ⋊ C2×C3 |
| derived, Sylow | C211 ⋊ C2×C3×C17 |
| Hall | C17×C211⋊C3 ⋊ C2 |
| Hall | C17×D211 ⋊ C3 |
| Hall | C211⋊C3 ⋊ C2×C17 |
| Hall | D211 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D211⋊C3 |
| commutator, cosocle, hypocenter | C211 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C211 | C2×C3 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3587 |
697 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21522, 10);