Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#92694⋊C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C3×#626 |
612 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222044, C2×AGL(1,𝔽7)×#626, C2×#72222040, … |
| maximal normal subgroup of | C2×#72222044, C2×AGL(1,𝔽7)×#626, C2×#72222040, … |
| maximal quotient of | #72269395 |
Past the SmallGroups library coverage — no SmallGroups id.