Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#63436 |
| Fitting | C22×C42×C9 ⋊ C2 |
| Sylow | C9 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini | C22×C3 | C24×D3 |
| Fitting | C22×C42×C9 | C2 |
| socle | C24×C3 | C22×D3 |
| hypercenter | C22×C42 | D9 |
| hypocenter | C9 | C22×#127 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
4500 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 4500 conjugacy classes of subgroups — too many to draw. Only its 1054 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 | C22×D9×#127, #72268892 |
| maximal normal subgroup of | C22×D9×#127, #72268892 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134707);