Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D3×2−1+4⋊C3 |
| unambiguous semidirect product | (D3×2−1+4)⋊C3 |
| Fitting | C3×2−1+4 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×A4 |
| commutator, cosocle, hypocenter | C3×Q8 | C23×C3 |
| Fitting | C3×2−1+4 | C2×C3 |
| socle | C2×C3 | C23×A4 |
| hypercenter | D4 | D3×A4 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C2 ◁ D4 | |
421 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5430, D3×#5431, #11922479, … |
| maximal normal subgroup of | D3×#5430, D3×#5431, #11922479, … |
| maximal quotient of | #85875⋊C3, #85878⋊C3, D3×#519⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8506);