Finite Group DatabasebetaFinite Group Databasebeta| order | 18816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C7 |
| direct product | #453×#64425 |
| Fitting | C72×#453 ⋊ C2×C3 |
| Hall | #453×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×#453 |
| Sylow | C72 ⋊ C2×C3×#453 |
4220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #453×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal normal subgroup of | #453×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.