Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D4×C3⋊D21 |
| Fitting | C2×C32×C7×D4 ⋊ C2 |
| Hall | C32×C7 ⋊ C22×D4 |
| Sylow | C32 ⋊ C2×D4×D7 |
| Sylow | C7 ⋊ C2×D4×C3⋊D3 |
1416 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×D7×C3⋊D3, C2×D4×C3⋊(C3⋊AGL(1,𝔽7)), #72245926, … |
| maximal normal subgroup of | C2×D4×D7×C3⋊D3, C2×D4×C3⋊(C3⋊AGL(1,𝔽7)), #72245926, … |
| maximal quotient of | #127×C3⋊D21, #120×C3⋊D21 |
Past the SmallGroups library coverage — no SmallGroups id.