Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×C8×D9 |
| Fitting | C23×C8×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D9 |
| commutator, hypocenter | C9 | C24×C8 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C23×C8×C9 | C2 |
| socle | C24×C3 | C4×D3 |
| prime radical | C24×D9 | C4 |
| cosocle | C4×C9 | C25 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C23×C8 | |
2964 conjugacy classes of subgroups; only the 1326 normal subgroups are shown.
This group has 2964 conjugacy classes of subgroups — too many to draw. Only its 1326 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152429);