Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D9 |
| Fitting | C22×C8×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D9 |
| commutator, hypocenter | C9 | C23×C8 |
| Frattini | C3×C4 | C23×D3 |
| Fitting | C22×C8×C9 | C2 |
| socle | C23×C3 | C4×D3 |
| prime radical | C23×D9 | C4 |
| cosocle | C4×C9 | C24 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C8 | |
507 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#336, #11783095, D9×#340, … |
| maximal normal subgroup of | D9×#336, #11783095, D9×#340, … |
| maximal quotient of | C2×C4×C8×D9, C22×C8×Dic9, C2×D9×C22⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1721);