Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of C11⋊((C24⋊C5)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C11⋊((C24⋊C5)⋊C2) |
| unambiguous semidirect product | (C24⋊C5)⋊D11 |
| Fitting, socle | C24×C11 ⋊ D5 |
| derived | C11×C24⋊C5 ⋊ C2 |
| Sylow | C11 ⋊ (C24⋊C5)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×C24⋊C5 | C2 |
| Fitting, socle | C24×C11 | D5 |
| LCS | G ▷ C11×C24⋊C5 | |
| UCS | C1 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
Polycyclic presentation:
2,5,11,2^4|b^a=b^4,c^a=c^10,d^a=defg,e^a=eg,f^a=fg,d^b=e,e^b=ef,f^b=fg,g^b=dg50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1271);