Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×D55 |
| Fitting | C5×D4×C11 ⋊ C2 |
| Hall | C5×C11 ⋊ C2×D4 |
| Sylow | C11 ⋊ D4×D5 |
| Sylow | C5 ⋊ D4×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D55 |
| commutator, socle, cosocle | C2×C5×C11 | C23 |
| Fitting | C5×D4×C11 | C2 |
| hypercenter | D4 | D55 |
| hypocenter | C5×C11 | C2×D4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
145 conjugacy classes — view the full character table.
| maximal subgroup of | #13182898, #13182904, #13182915, … |
| maximal normal subgroup of | #13182898, #13182904, #13182915, … |
| maximal quotient of | #13183177, #13183178, C22⋊C4×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 200);