Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8 |
| direct product | C8×#812 |
| Sylow | C3 ⋊ C8×M32 |
354 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C8×M32, #72225829, #72225843, … |
| maximal normal subgroup of | D3×C8×M32, #72225829, #72225843, … |
| maximal quotient of | #72225829 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 78547);