Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#85469 |
| Fitting | C3×#577 ⋊ D3 |
526 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11923456, C3×#11715001, D3×#85469, … |
| maximal normal subgroup of | C3×#11715001, D3×#85469, #72242438 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156764);