Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×Q8×S4 |
| Fitting | C22×C3×Q8 ⋊ D3 |
324 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#215, #11922202, S4×#216, … |
| maximal normal subgroup of | S4×#215, #11922202, S4×#216, … |
| maximal quotient of | C3×#85302, C3×#85311, C3×#85303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8442);