Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#73035 |
| Fitting | C23×C16 ⋊ D3 |
437 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 437 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #72342690, C2×S4×D16, #72342792, … |
| maximal normal subgroup of | #72342690, C2×S4×D16, #72342792, … |
| maximal quotient of | #72342818 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088569);