Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #4341⋊C5 |
| Fitting | D4×C11 ⋊ C2×C5 |
| Hall | #4341 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #41 |
| Sylow | C11 ⋊ C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×AGL(1,𝔽11) |
| commutator, socle, cosocle | C2×C11 | C23×C5 |
| Fitting | D4×C11 | C2×C5 |
| hypercenter | D4 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#41 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ D4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^3,5,2,11|b^2=e,c^a=ce,f^a=f^10,c^b=ce,f^d=f^955 conjugacy classes — view the full character table.
| maximal subgroup of | #66964⋊C5, #66965⋊C5, #66968⋊C5, … |
| maximal normal subgroup of | #66964⋊C5, #66965⋊C5, #66968⋊C5, … |
| maximal quotient of | #66930⋊C5, #66931⋊C5, #66938⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 119);