Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #63626 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×#63626 |
| Fitting | C22×C32×C16 ⋊ C2 |
| Sylow | C32 ⋊ C22×D16 |
1320 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 345 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11797813, C22×C3⋊D3×D16, C2×#11797807 |
| maximal normal subgroup of | C2×#11797813, C22×C3⋊D3×D16, C2×#11797807 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133446);