Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #3672 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#3675 |
| Fitting | C23×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ C23×SD16 |
2580 conjugacy classes of subgroups; only the 814 normal subgroups are shown.
This group has 2580 conjugacy classes of subgroups — too many to draw. Only its 814 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152560);