Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C11 ⋊ #131 |
| Sylow | C11 ⋊ #4094 |
| Sylow | C5 ⋊ #67001 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D55 |
| commutator, socle | C2×C5×C11 | C22×C4 |
| Fitting, prime radical | C5×C11×#41 | C2 |
| cosocle | C4×C5×C11 | C23 |
| hypercenter | #41 | D55 |
| hypocenter | C5×C11 | #131 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C4 ◁ #41 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 880 |
Polycyclic presentation:
2^5,5,11|a^2=d,d^2=e,f^a=f^4,g^a=g^10,c^b=ce290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1056);