Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C22×C22⋊C4×D9 |
| Fitting | C22×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ C23×C22⋊C4 |
6948 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#1898, D9×#1438, D9×#1437, … |
| maximal normal subgroup of | D9×#1898, D9×#1438, D9×#1437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133811);