Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | D4×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×D4) |
| unambiguous semidirect product | (D4×D11)⋊C5 |
| Fitting | D4×C11 ⋊ C2×C5 |
| Hall | D4×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D4 |
| Sylow | C11 ⋊ C2×C5×D4 |
| 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 | C2×C5×D4 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
55 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 118);