Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C8×#3745 |
| Fitting | C32×C82 ⋊ C2 |
| Sylow | C32 ⋊ C8×D8 |
588 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72254878, C8×D8×C3⋊D3, #72254921, … |
| maximal normal subgroup of | #72254878, C8×D8×C3⋊D3, #72254921, … |
| maximal quotient of | #72254878 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 11154);