Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C82⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C8 |
| direct product | C3×C82⋊C3 |
| unambiguous semidirect product | C82⋊C32 |
| unambiguous semidirect product | (C3×C82)⋊C3 |
| Fitting | C3×C82 ⋊ C3 |
| derived, Sylow | C82 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C82⋊C3 |
| commutator, cosocle, hypocenter | C82 | C32 |
| Frattini | C42 | C3×A4 |
| Fitting | C3×C82 | C3 |
| socle | C22×C3 | C42⋊C3 |
| LCS | G ▷ C82 | |
| UCS | C1 ◁ C3 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1070);