Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×D3×2−1+4 |
| Fitting | C32×2−1+4 ⋊ C2 |
| Sylow | C32 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C24×D3 |
| commutator, cosocle | C2×C3 | C25×C3 |
| Frattini | C2 | C24×C3×D3 |
| Fitting | C32×2−1+4 | C2 |
| socle | C2×C32 | C25 |
| hypercenter | C3×2−1+4 | D3 |
| hypocenter | C3 | C2×C3×2−1+4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C3 ◁ C3×2−1+4 | |
1661 conjugacy classes of subgroups; only the 890 normal subgroups are shown.
This group has 1661 conjugacy classes of subgroups — too many to draw. Only its 890 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#454, D3×#5245, C3×D3×#456, … |
| maximal normal subgroup of | C3×D3×#454, D3×#5245, C3×D3×#456, … |
| maximal quotient of | C3×D3×#519, C3×D3×#520, C3×#85873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8621);