Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of C22⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊(C42⋊C3) |
| Fitting, Sylow | C22×C43 ⋊ C3 |
| derived | C22×C42 ⋊ C3×C4 |
1409 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 1409 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11709197, #72237318, #72237322, … |
| maximal normal subgroup of | #72237322, C4×#85547, #72239820, … |
| maximal quotient of | C4×#11709197, #72239403, C4×#11709219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084112);