Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23×C3 |
| direct product | C16×C4⋊(C3⋊D3) |
| Fitting | C32×C4×C16 ⋊ C2 |
| Sylow | C32 ⋊ D4×C16 |
522 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #72269802 |
| maximal normal subgroup of | #72269802 |
| maximal quotient of | #72269802 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31449);