Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×D3×C8 |
| Fitting | C22×C32×C8 ⋊ C2 |
| derived | C3 ⋊ C23×C3×C8 |
| Sylow | C32 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C8 | D3 |
| commutator, hypocenter | C3 | C23×C3×C8 |
| Frattini | C4 | C23×C3×D3 |
| Fitting | C22×C32×C8 | C2 |
| socle | C23×C32 | C2×C4 |
| prime radical | C23×C3×D3 | C4 |
| cosocle | C3×C4 | C24×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C3×C8 | |
714 conjugacy classes of subgroups; only the 414 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 414 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#336, D3×#4550, C3×#68661, … |
| maximal normal subgroup of | C3×D3×#336, D3×#4550, C3×#68661, … |
| maximal quotient of | C2×C3×C4×D3×C8, C22×C3×C8×Dic3, C2×C3×D3×C22⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7715);