Finite Group DatabasebetaFinite Group Databasebeta| order | 612 |
| isoclinism | isoclinic class of D9×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D17 |
| unambiguous semidirect product | (C17×D9)⋊C2 |
| unambiguous semidirect product | (C9×D17)⋊C2 |
| unambiguous semidirect product | D153⋊C2 |
| Fitting, derived, Hall | C9×C17 ⋊ C22 |
| Sylow | C17 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C17 | C22 |
| Frattini | C3 | D3×D17 |
| socle | C3×C17 | C2×D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 153 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#595, C2×D9×D17, D17×D27, … |
| maximal normal subgroup of | D9×#595, C2×D9×D17, C3×D9×D17, … |
| maximal quotient of | #11927434, D9×Dic17, #11927436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(612, 7);