Finite Group DatabasebetaFinite Group Databasebeta| order | 3402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | D7×#6909 |
| Fitting, Hall | C7×#6909 ⋊ C2 |
| Sylow | C7 ⋊ C2×#6909 |
296 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 189 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#10624749, AGL(1,𝔽7)×#6909, #72249140, … |
| maximal normal subgroup of | D7×#10624749, AGL(1,𝔽7)×#6909, #72249140, … |
Past the SmallGroups library coverage — no SmallGroups id.