Finite Group DatabasebetaFinite Group Databasebeta| order | 16461 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×C31⋊C9 |
| unambiguous semidirect product | C31⋊(C9×C59) |
| unambiguous semidirect product | (C31×C59)⋊C9 |
| derived, Sylow | C31 ⋊ C9×C59 |
| Hall | C31×C59 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C59 | C31⋊C3 |
| commutator, hypocenter | C31 | C9×C59 |
| Frattini | C3 | C59×C31⋊C3 |
| Fitting, socle, prime radical | C3×C31×C59 | C3 |
| cosocle | C3×C31 | C3×C59 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C59 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16461 |
2301 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C59×C31⋊C9, D59×C31⋊C9, C59×D31⋊C9, … |
| maximal normal subgroup of | C2×C59×C31⋊C9, D59×C31⋊C9, C59×D31⋊C9, … |
| maximal quotient of | C2×C59×C31⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16461, 2);