Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | D4×D5×C11 |
| Fitting | C5×D4×C11 ⋊ C2 |
| Hall | C5×C11 ⋊ C2×D4 |
| Sylow | C5 ⋊ C2×D4×C11 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11 | C22×D5 |
| commutator, cosocle | C2×C5 | C23×C11 |
| Frattini | C2 | C22×D5×C11 |
| Fitting | C5×D4×C11 | C2 |
| socle | C2×C5×C11 | C23 |
| hypercenter | D4×C11 | D5 |
| hypocenter | C5 | C2×D4×C11 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C11 ◁ D4×C11 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#4007, #13182654, D5×#4323, … |
| maximal normal subgroup of | C11×#4007, #13182654, D5×#4323, … |
| maximal quotient of | C11×#4024, C11×#4031, D5×C11×C22⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 190);