Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D55 |
| Fitting, socle | C23×C5×C11 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C24 |
| Sylow | C11 ⋊ C23×D5 |
| Sylow | C5 ⋊ C23×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D55 |
| commutator, cosocle, hypocenter | C5×C11 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C5×C11 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C23 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11724886, #13182973, #13182986, … |
| maximal normal subgroup of | C2×#11724886, #13182973, #13182986, … |
| maximal quotient of | C22×Dic110, C22×C4×D55, C22×D220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 220);