Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×C9⋊C8 |
| unambiguous semidirect product | C9⋊C82 |
| derived, Sylow | C9 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D9 |
| commutator, hypocenter | C9 | C82 |
| Frattini | C3×C42 | C2×D3 |
| Fitting | C4×C8×C9 | C2 |
| socle, prime radical | C22×C3 | C4×Dic3 |
| cosocle | C42×C9 | C22 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C4×C8 | |
111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C16×C9⋊C8, #11771293, #11771308, … |
| maximal normal subgroup of | C16×C9⋊C8, #11771293, #11771308, … |
| maximal quotient of | C9⋊#1273, C16×C9⋊C8, C8×C9⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 12);