Finite Group DatabasebetaFinite Group Databasebeta| order | 8349 |
| isoclinism | isoclinic class of C112⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C11 |
| direct product | C23×C112⋊C3 |
| unambiguous semidirect product | C112⋊(C3×C23) |
| unambiguous semidirect product | (C112×C23)⋊C3 |
| Fitting, socle, Hall | C112×C23 ⋊ C3 |
| derived, Sylow | C112 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C112⋊C3 |
| commutator, hypocenter | C112 | C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
989 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8349, 5);