Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×Q8⋊C8 |
| Fitting | C32×Q8⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ C2×Q8⋊C8 |
840 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 8204);