Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C11 ⋊ C4⋊Q8 |
| Sylow | C11 ⋊ #4090 |
| Sylow | C5 ⋊ #66997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D55 |
| commutator, socle, prime radical, cosocle | C22×C5×C11 | C23 |
| Fitting | C2×C5×Q8×C11 | C2 |
| hypercenter | C2×Q8 | D55 |
| hypocenter | C5×C11 | C4⋊Q8 |
| LCS | G ▷ C22×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1760 |
Polycyclic presentation:
2^5,5,11|a^2=e,b^2=e,c^2=e,b^a=be,c^a=cd,f^a=f^4,g^a=g^10,c^b=ce284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1049);