Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14582089 |
| unambiguous semidirect product | (C2×#14582089)⋊C2 |
| Fitting | C22×C673 ⋊ C4 |
| Sylow | C673 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=d,b^a=bc,e^a=e^58,e^d=e^672682 conjugacy classes — view the full character table.
| maximal subgroup of | #36340535, #36340536, C2×C22⋊#14582089, … |
| maximal normal subgroup of | #36340535, #36340536, C2×C22⋊#14582089, … |
| maximal quotient of | (C2×#14582089)⋊C4, C22⋊#19129094, #36340534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 45);