Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4⋊C4×C22⋊A4 |
| unambiguous semidirect product | C4⋊(C4×C22⋊A4) |
| Fitting, Sylow | C24×C4⋊C4 ⋊ C3 |
3442 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 3442 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) = 48 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C4×#1020, A42×C4⋊C4, #106×C22⋊A4, … |
| maximal normal subgroup of | C4⋊C4×#1020, A42×C4⋊C4, #106×C22⋊A4, … |
| maximal quotient of | #72227310, #72227316, #106×C22⋊A4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084959);