Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C3×C42 |
| direct product | C4×#63642 |
| Sylow | C32 ⋊ C4×#97 |
1080 conjugacy classes of subgroups; only the 561 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 561 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1152 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C3⋊D3×#97 |
| maximal normal subgroup of | C4×C3⋊D3×#97 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17031);