Finite Group DatabasebetaFinite Group Databasebeta| order | 8244 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#11745021⋊C3 |
| unambiguous semidirect product | #11745021⋊C32 |
| unambiguous semidirect product | (C3×#11745021)⋊C3 |
| Fitting, socle | C3×C229 ⋊ C3×C4 |
| derived, Sylow | C229 ⋊ C32×C4 |
| Hall | C3×C229⋊C3 ⋊ C4 |
| Hall | #11745021 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11745021⋊C3 |
| commutator, hypocenter | C229 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C229 | C3×C4 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8244, 30);