Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#10589365 |
| Sylow | C32 ⋊ C2×M64 |
336 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 257 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11772675, C2×C3⋊D3×M64, C2×#11772672 |
| maximal normal subgroup of | C2×#11772675, C2×C3⋊D3×M64, C2×#11772672 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34471);