Finite Group DatabasebetaFinite Group Databasebeta| order | 2420 |
| isoclinism | isoclinic class of D11×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic11×C11⋊C5 |
| derived, Sylow | C112 ⋊ C4×C5 |
| Hall | C11×C11⋊C5 ⋊ C4 |
| Hall | C11×Dic11 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D11×C11⋊C5 |
| commutator, hypocenter | C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C112 | C2×C5 |
| prime radical | C2×C11×C11⋊C5 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 220 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2420, 27);