Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D11×C22⋊D5 |
| Fitting | C22×C5×C11 ⋊ C22 |
| Hall | C5×C11 ⋊ C2×D4 |
| Sylow | C11 ⋊ C2×C22⋊D5 |
| Sylow | C5 ⋊ D4×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×D11 |
| commutator, socle, cosocle | C2×C5×C11 | C23 |
| Fitting | C22×C5×C11 | C22 |
| hypercenter | C22 | D5×D11 |
| hypocenter | C5×C11 | C2×D4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#709, #13183377, D4×D5×D11, … |
| maximal normal subgroup of | D11×#709, #13183377, D4×D5×D11, … |
| maximal quotient of | D11×#683, #13182803, #13182804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 173);