Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×#821 |
| Fitting | C2×C32×C8 ⋊ C22 |
| Sylow | C32 ⋊ C2×#102 |
429 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#102, C2×D3×#821, D3×#5113, … |
| maximal normal subgroup of | D32×#102, C2×D3×#821, D3×#5113, … |
| maximal quotient of | D3×#4459, #11774376, #11774562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2820);