Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#73049 |
| Fitting | C23×C22⋊C4 ⋊ D3 |
1355 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 1355 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11713202, C2×S4×#99, C2×#11713362 |
| maximal normal subgroup of | C2×#11713202, C2×S4×#99, C2×#11713362 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087133);