Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C2×C3×#1007 |
| Fitting | C22×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C2×2−1+4 |
1666 conjugacy classes of subgroups; only the 894 normal subgroups are shown.
This group has 1666 conjugacy classes of subgroups — too many to draw. Only its 894 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69692, C3×#70121, #11784904, … |
| maximal normal subgroup of | C3×#69692, C3×#70121, #11784904, … |
| maximal quotient of | C2×C3×#5572, C2×C3×#5812, C2×C3×#5504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8614);