Finite Group DatabasebetaFinite Group Databasebeta| order | 1521 |
| isoclinism | isoclinic class of #92788 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#92788 |
| Fitting, socle | C3×C132 ⋊ C3 |
| derived, Sylow | C132 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92788 |
| commutator, cosocle, hypocenter | C132 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 507 |
177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11759815, C3×#11759817, C3⋊#11759815, … |
| maximal normal subgroup of | C3×#11759815, C3×#11759817, C3⋊#11759815, … |
| maximal quotient of | C2×C3×#92788, C3×C11×#92788, C3×C17×#92788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1521, 11);