Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic11⋊C5 |
| unambiguous semidirect product | (C11⋊C5)⋊C42 |
| unambiguous semidirect product | (C4×Dic11)⋊C5 |
| derived, Sylow | C11 ⋊ C42×C5 |
| Hall | C4×Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C42×C5 |
| Frattini | C22 | C2×AGL(1,𝔽11) |
| Fitting | C2×C4×C11 | C2×C5 |
| socle, cosocle | C22×C11 | C22×C5 |
| prime radical | C22×C11⋊C5 | C22 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Dic11⋊C5, (Dic11⋊C5)⋊C8, #66879⋊C5, … |
| maximal normal subgroup of | C8×Dic11⋊C5, (Dic11⋊C5)⋊C8, #66879⋊C5, … |
| maximal quotient of | C4×(C11⋊C5)⋊C8, #66867⋊C5, C8×Dic11⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 14);