Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic9 |
| derived, Sylow | C9 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D9 |
| commutator, hypocenter | C9 | C2×C4×C8 |
| Frattini | C2×C3×C4 | C22×D3 |
| Fitting | C22×C8×C9 | C2 |
| socle, prime radical | C23×C3 | C4×D3 |
| cosocle | C2×C4×C9 | C23 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C8 | |
243 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #11772257, #11772289, C4×C8×Dic9, … |
| maximal normal subgroup of | #11772257, #11772289, C4×C8×Dic9, … |
| maximal quotient of | C2×C8×C9⋊C8, C2×#10588131, C8×#3667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 661);