Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#5211 |
| Sylow | C32 ⋊ #381 |
554 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 174 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×#67616, C3×#67682, #11770884, … |
| maximal normal subgroup of | C3×#67616, C3×#67682, #11770884, … |
| maximal quotient of | C3×#72127, C3×#71534, C3×#71548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4190);