Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C24×C4⋊Dic3 |
| Sylow | C3 ⋊ C24×C4⋊C4 |
19742 conjugacy classes of subgroups; only the 13003 normal subgroups are shown.
This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 13003 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 768 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076123);