Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C9⋊C32 |
| unambiguous semidirect product | (C2×C9)⋊C32 |
| derived, Sylow | C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D9 |
| commutator, hypocenter | C9 | C2×C32 |
| Frattini | C3×C16 | C2×D3 |
| Fitting | C2×C9×C16 | C2 |
| socle, prime radical | C22×C3 | C3⋊C16 |
| cosocle | C9×C16 | C22 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C16 | |
51 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C32×Dic9, C4×C9⋊C32, #11772657, … |
| maximal normal subgroup of | C32×Dic9, C4×C9⋊C32, #11772657, … |
| maximal quotient of | C4×C9⋊C32, #11772688, C4⋊(C9⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 57);