Finite Group DatabasebetaFinite Group Databasebeta| order | 22001 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C449⋊C7 |
| unambiguous semidirect product | C449⋊C72 |
| unambiguous semidirect product | (C7×C449)⋊C7 |
| Fitting, socle | C7×C449 ⋊ C7 |
| derived, Sylow | C449 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C449⋊C7 |
| commutator, cosocle, hypocenter | C449 | C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C449 | C7 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3143 |
497 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22001, 3);