Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic36 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63364 |
| Fitting | C2×C42×C9 ⋊ C2 |
| Sylow | C9 ⋊ C2×#104 |
255 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11783856, C4×#63364, #11783890, … |
| maximal normal subgroup of | #11783856, C4×#63364, #11783890, … |
| maximal quotient of | C2×#10588136, C2×#10588133, #11774234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 489);