Finite Group DatabasebetaFinite Group Databasebeta| order | 10512 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽73) |
| Fitting, socle | C2×C73 ⋊ C8×C9 |
| derived, Sylow | C73 ⋊ C2×C8×C9 |
| Hall | C2×#10596842 ⋊ C9 |
| Hall | #10620323 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽73) |
| commutator, hypocenter | C73 | C2×C8×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C73 | C8×C9 |
| prime radical | C2×D73⋊C3 | C3×C4 |
| cosocle | #64408⋊C3 | C22×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 146 |
146 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽73) |
| maximal quotient of | D3×AGL(1,𝔽73) |
| holomorph of | C2×C73 |
Past the SmallGroups library coverage — no SmallGroups id.