Finite Group DatabasebetaFinite Group Databasebeta| order | 23226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#26042470 |
| Fitting, Hall | C2×C49×C79 ⋊ C3 |
| derived, Hall | C49×C79 ⋊ C2×C3 |
| Hall | C2×C79 ⋊ C49⋊C3 |
| Hall | C2×C49 ⋊ C79⋊C3 |
| Sylow | C79 ⋊ C2×C49⋊C3 |
| Sylow | C49 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #26042470 |
| commutator, cosocle, hypocenter | C49×C79 | C2×C3 |
| Frattini | C7 | C2×#13110305 |
| Fitting | C2×C49×C79 | C3 |
| socle | C2×C7×C79 | ΓL(1,𝔽8) |
| LCS | G ▷ C49×C79 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7742 |
2586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23226, 4);