Finite Group DatabasebetaFinite Group Databasebeta| order | 711 |
| isoclinism | isoclinic class of C79⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊C9 |
| derived, Sylow | C79 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C79⋊C3 |
| commutator, hypocenter | C79 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C79 | C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 88 |
| transitive degree | μt(G) = 711 |
Polycyclic presentation:
3^2,79|a^3=b,c^a=c^2387 conjugacy classes — view the full character table.
| maximal subgroup of | D79⋊C9, C2×C79⋊C9, C9×C79⋊C3, … |
| maximal normal subgroup of | D79⋊C9, C2×C79⋊C9, C9×C79⋊C3, … |
| maximal quotient of | C2×C79⋊C9, C79⋊C27, C3×C79⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(711, 1);