Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C9⋊C16 |
| derived, Sylow | C9 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D9 |
| commutator, hypocenter | C9 | C22×C16 |
| Frattini | C3×C8 | C22×D3 |
| Fitting | C22×C8×C9 | C2 |
| socle, prime radical | C23×C3 | C3⋊C8 |
| cosocle | C8×C9 | C23 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C8 | |
147 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #11772257, #11772260, #11772346, … |
| maximal normal subgroup of | #11772257, #11772260, #11772346, … |
| maximal quotient of | C2×C4×C9⋊C16, C2×#10588226, C2×C4⋊(C9⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 658);