Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×A4×#123 |
| unambiguous semidirect product | (C23×#123)⋊C3 |
| Fitting, Sylow | C23×#123 ⋊ C3 |
3095 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 3095 conjugacy classes of subgroups — too many to draw. Only its 267 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×#560, C2×#72214004, #72258949 |
| maximal normal subgroup of | C2×A4×#560 |
| maximal quotient of | C2×#72214004, #72258949 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084992);