Finite Group DatabasebetaFinite Group Databasebeta| order | 612 |
| isoclinism | isoclinic class of C9⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#595 |
| Fitting, derived, Hall | C9×C17 ⋊ C4 |
| Sylow | C17 ⋊ Dic9 |
| Sylow | C9 ⋊ #595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C17 | C4 |
| Frattini | C3 | C3⋊#595 |
| socle | C3×C17 | Dic3 |
| prime radical | C3×D17 | D3 |
| cosocle | C9×D17 | C2 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 153 |
Polycyclic presentation:
2^2,3,17,3|a^2=b,c^3=e,c^a=c^2e^2,d^a=d^4,e^a=e^2,d^b=d^1648 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#595, C2×C9⋊#595, C27⋊#595, … |
| maximal normal subgroup of | D9×#595, C2×C9⋊#595, C3×C9⋊#595, … |
| maximal quotient of | C9⋊#3624, C2×C9⋊#595, C27⋊#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(612, 6);