Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C7 |
| direct product | C3×D4×C7⋊D7 |
| Fitting | C3×C72×D4 ⋊ C2 |
| Hall | C3×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
540 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 588 |
390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D4×C7⋊D7, C2×C3×D4×C7⋊D7, C3×D4×#64424, … |
| maximal normal subgroup of | D3×D4×C7⋊D7, C2×C3×D4×C7⋊D7, C3×D4×#64424, … |
| maximal quotient of | C2×C3×D4×C7⋊D7 |
Past the SmallGroups library coverage — no SmallGroups id.