Finite Group DatabasebetaFinite Group Databasebeta| order | 22001 |
| automorphism | ? |
| homology | Abelianization (H1) = C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C449⋊C49 |
| derived, Sylow | C449 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | C449⋊C7 |
| commutator, hypocenter | C449 | C49 |
| Fitting, socle, prime radical, cosocle | C7×C449 | C7 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C7 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22001 |
Polycyclic presentation:
7^2,449|a^7=b,c^a=c^324497 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22001, 1);