Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C22⋊C4×C22⋊A4 |
| Fitting, Sylow | C24×C22⋊C4 ⋊ C3 |
7478 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 7478 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #120×C22⋊A4, C22⋊C4×#1020, #72216649, … |
| maximal normal subgroup of | #120×C22⋊A4, C22⋊C4×#1020, #72216649, … |
| maximal quotient of | #72227330, #72246701, #72247524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084958);