Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#4718 |
| Sylow | C32 ⋊ #431 |
261 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68100, C3×#68124, #11773762, … |
| maximal normal subgroup of | C3×#68100, C3×#68124, #11773762, … |
| maximal quotient of | C3×#68596, C3×Dic3×C22⋊C8, C3×#68602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3697);