Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C22×#63774 |
| Fitting | C23×C32×C4 ⋊ C4 |
| Sylow | C32 ⋊ C22×#99 |
2474 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 2474 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91503);