Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5580 |
| Fitting | C32×C4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ #529 |
503 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68233, #11774442, C3×#68234, … |
| maximal normal subgroup of | C3×#68233, #11774442, C3×#68234, … |
| maximal quotient of | C3×#73752, C3×#73754, C3×#73617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7559);