Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of D11⋊(C24⋊C5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D11⋊(C24⋊C5) |
| unambiguous semidirect product | (C11⋊(C24⋊C5))⋊C2 |
| Fitting, socle, derived | C24×C11 ⋊ C2×C5 |
| Hall | C24×D11 ⋊ C5 |
| Sylow | C11 ⋊ C2×C24⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C11 | C2×C5 |
| LCS | G ▷ C24×C11 | |
| UCS | C1 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
Polycyclic presentation:
2,5,2^4,11|g^a=g^10,c^b=cd,d^b=ce,e^b=cdef,f^b=cdf,g^b=g^932 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1274);