Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×C3⋊C16 |
| derived | C3 ⋊ C22×C3×C16 |
| Sylow | C32 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C8 | D3 |
| commutator, hypocenter | C3 | C22×C3×C16 |
| Frattini | C8 | C22×C3×D3 |
| Fitting | C22×C32×C8 | C2 |
| socle, prime radical | C23×C32 | C8 |
| cosocle | C3×C8 | C23×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C3×C8 | |
234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#67804, C3×#67657, #11772266, … |
| maximal normal subgroup of | C3×#67804, C3×#67657, #11772266, … |
| maximal quotient of | C2×C3×C4×C3⋊C16, C2×C3×#4549, C2×C3×C4⋊(C3⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4075);