Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#6104⋊C3 |
| unambiguous semidirect product | (C2×#6104)⋊C3 |
| Fitting | C2×D4×C13 ⋊ C2×C3 |
| Hall | C2×#6104 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×D8 |
| Sylow | C13 ⋊ C2×C3×D8 |
152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
62 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D8×D13⋊C3, #72276135, #72276142 |
| maximal normal subgroup of | C2×D8×D13⋊C3, #72276135, #72276142 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 413);