Finite Group DatabasebetaFinite Group Databasebeta| order | 9312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#72210656 |
| Fitting, socle | C2×C97 ⋊ C3×C16 |
| derived, Sylow | C97 ⋊ C2×C3×C16 |
| Hall | C2×#13095525 ⋊ C3 |
| Hall | C97⋊C3 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72210656 |
| commutator, hypocenter | C97 | C2×C3×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C97 | C3×C16 |
| prime radical | C2×D97⋊C3 | C8 |
| cosocle | #11715906 | C22×C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
100 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210656, C2×AGL(1,𝔽97) |
| maximal normal subgroup of | C2×AGL(1,𝔽97) |
| maximal quotient of | D3×#72210656 |
Past the SmallGroups library coverage — no SmallGroups id.