Finite Group DatabasebetaFinite Group Databasebeta| order | 578 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D17 |
| unambiguous semidirect product | C17⋊(C2×C17) |
| Fitting, socle, Sylow | C172 ⋊ C2 |
| derived | C17 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C172 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#595, #11923885, D172, … |
| maximal normal subgroup of | C17×#595, #11923885, D172, … |
| maximal quotient of | C17×Dic17, C2×C17×D17, C17×D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(578, 3);