Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊#168 |
| unambiguous semidirect product | (C2×C11)⋊#168 |
| derived, Hall | C5×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ C2×#168 |
| Sylow | C5 ⋊ C2×C11⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D55 |
| commutator, hypocenter | C5×C11 | C2×C8 |
| Frattini | C4 | C2×D55 |
| Fitting | C2×C4×C5×C11 | C2 |
| socle, prime radical | C22×C5×C11 | C4 |
| cosocle | C4×C5×C11 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2×C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 880 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | #168×Dic11, Dic5×C11⋊C8, #13182281, … |
| maximal normal subgroup of | #168×Dic11, Dic5×C11⋊C8, #13182281, … |
| maximal quotient of | C4×C11⋊#168, C4⋊(C11⋊#168), C2×C11⋊#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 95);