Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×D8×D9 |
| Fitting | C22×C9×D8 ⋊ C2 |
| Sylow | C9 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D9 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C22×C9×D8 | C2 |
| socle | C23×C3 | D3×D4 |
| hypercenter | C22×D8 | D9 |
| hypocenter | C9 | C23×D8 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
2964 conjugacy classes of subgroups; only the 654 normal subgroups are shown.
This group has 2964 conjugacy classes of subgroups — too many to draw. Only its 654 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152539);