Finite Group DatabasebetaFinite Group Databasebeta| order | 1521 |
| isoclinism | isoclinic class of #92789 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Sylow | C132 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #92789 |
| commutator, hypocenter | C132 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C132 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 117 |
Polycyclic presentation:
3^2,13^2|a^3=b,c^a=c^3,d^a=d^9177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1521, 7);