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 | C23×C3×C3⋊C8 |
| derived | C3 ⋊ C23×C3×C8 |
| Sylow | C32 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3×C4 | D3 |
| commutator, hypocenter | C3 | C23×C3×C8 |
| Frattini | C4 | C23×C3×D3 |
| Fitting | C23×C32×C4 | C2 |
| socle, prime radical | C24×C32 | C4 |
| cosocle | C3×C4 | C24×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C23×C3×C4 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#4550, C2×C3×#4524, C2×#10589155, … |
| maximal normal subgroup of | C2×C3×#4550, C2×C3×#4524, C2×#10589155, … |
| maximal quotient of | C22×C3×C4×C3⋊C8, C22×C3×#830, C22×C3×C4⋊(C3⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7759);