Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of D11×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D11×C11⋊C5 |
| Fitting, socle, derived, Sylow | C112 ⋊ C2×C5 |
| Hall | C11×C11⋊C5 ⋊ C2 |
| Hall | C11×D11 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
17 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 110 |
49 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 17);