Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C11⋊AGL(1,𝔽5)) |
| Fitting | C4×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ C4⋊C4 |
| Sylow | C11 ⋊ C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4⋊Dic11 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
Polycyclic presentation:
2^4,5,11|a^2=c,b^2=d,b^a=bd,e^a=e^3,f^a=f^10,e^c=e^494 conjugacy classes — view the full character table.
| maximal subgroup of | #13182560, #13182562, #13182567, … |
| maximal normal subgroup of | #13182560, #13182562, #13182567, … |
| maximal quotient of | #13182639, #13182640, #13182641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 145);