Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#875 |
| Fitting | C32×C42 ⋊ C22 |
| Sylow | C32 ⋊ C2×#124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting | C32×C42 | C22 |
| prime radical | C2×D3×D12 | C2 |
| hypercenter | C42 | D32 |
| hypocenter | C32 | C2×#124 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C42 | |
698 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 160 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 | D3×#4464, #11775785, #11775792, … |
| maximal normal subgroup of | D3×#4464, #11775785, #11775792, … |
| maximal quotient of | D3×#4936, D3×#4940, D3×#4939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5881);