Finite Group DatabasebetaFinite Group Databasebeta| order | 22379 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C7×C139⋊C23 |
| unambiguous semidirect product | C139⋊(C7×C23) |
| unambiguous semidirect product | (C7×C139)⋊C23 |
| Fitting, socle, Hall | C7×C139 ⋊ C23 |
| derived, Sylow | C139 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C139⋊C23 |
| commutator, cosocle, hypocenter | C139 | C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C139 | C23 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 973 |
203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22379, 1);