Finite Group DatabasebetaFinite Group Databasebeta| order | 2420 |
| isoclinism | isoclinic class of D11×D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D55 |
| unambiguous semidirect product | (C5×D11)⋊D11 |
| unambiguous semidirect product | (C11×D11)⋊D5 |
| Fitting, socle, derived, Hall | C5×C112 ⋊ C22 |
| Sylow | C112 ⋊ C2×D5 |
| Sylow | C5 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C112 | C22 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
203 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D275, #11925895⋊D5, #11925896⋊D5, … |
| maximal normal subgroup of | #11925895⋊D5, #11925896⋊D5, #11925897⋊D5, … |
| maximal quotient of | D11×D275, C5×D11×D55, D11×C5⋊D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2420, 68);