Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#5095 |
| Fitting | C32×C4⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ #456 |
318 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 318 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) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67550, C3×#67463, #11772788, … |
| maximal normal subgroup of | C3×#67550, C3×#67463, #11772788, … |
| maximal quotient of | C3×#69705, C3×#69706, C3×#69707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4074);