Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic9 |
| derived, Sylow | C9 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D9 |
| commutator, hypocenter | C9 | C24×C4 |
| Frattini | C2×C3 | C24×D3 |
| Fitting | C25×C9 | C2 |
| socle, prime radical | C25×C3 | D3 |
| cosocle | C2×C9 | C25 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C25 | |
2043 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #11773153, C22×C9⋊#95, C2×C22⋊C4×Dic9, … |
| maximal normal subgroup of | #11773153, C22×C9⋊#95, C2×C22⋊C4×Dic9, … |
| maximal quotient of | C23×C4×Dic9, C23×#3676, C23×C4⋊Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5026);