Finite Group DatabasebetaFinite Group Databasebeta| order | 873 |
| isoclinism | isoclinic class of C97⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C97⋊C9 |
| derived, Sylow | C97 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C97⋊C3 |
| commutator, hypocenter | C97 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C97 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 106 |
| transitive degree | μt(G) = 873 |
Polycyclic presentation:
3^2,97|a^3=b,c^a=c^35105 conjugacy classes — view the full character table.
| maximal subgroup of | D97⋊C9, C2×C97⋊C9, C9×C97⋊C3, … |
| maximal normal subgroup of | D97⋊C9, C2×C97⋊C9, C9×C97⋊C3, … |
| maximal quotient of | C2×C97⋊C9, C97⋊C27, C3×C97⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(873, 1);