Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C25 |
| direct product | C3×#82007 |
| Fitting | C2×C32×M32 ⋊ C2 |
| Sylow | C32 ⋊ #3407 |
765 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72222733, C3×#10947846, #72222740, … |
| maximal normal subgroup of | #72222733, C3×#10947846, #72222740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133420);