Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5032 |
| Fitting | C32×#120 ⋊ C2 |
| Sylow | C32 ⋊ B(4,𝔽2) |
461 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71909, C3×#69130, #11798530, … |
| maximal normal subgroup of | C3×#71909, C3×#69130, #11798530, … |
| maximal quotient of | C3×#70968, C3×#69696, C3×#70976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4011);