Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#5401 |
| Fitting | C22×C3×C8 ⋊ D3 |
152 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #11921782, D3×#5401, #11921790, … |
| maximal normal subgroup of | #11921782, D3×#5401, #11921790, … |
| maximal quotient of | C3×#73012, C3×#73011, C3×#73021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5469);