Finite Group DatabasebetaFinite Group Databasebeta| order | 22358 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1597⋊C7 |
| unambiguous semidirect product | (C1597⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C1597 ⋊ C2×C7 |
| Hall | C1597⋊C7 ⋊ C2 |
| Hall | D1597 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1597 | C2×C7 |
| LCS | G ▷ C1597 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1597 |
Polycyclic presentation:
2,7,1597|c^a=c^1596,c^b=c^1150128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22358, 1);