Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C11×C11⋊C5 |
| unambiguous semidirect product | (C2×C11)⋊(C5×C11) |
| Fitting, socle, Hall | C2×C112 ⋊ C5 |
| derived | C11 ⋊ C2×C5×C11 |
| Sylow | C112 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 18);