Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C29×#106 ⋊ C2 |
| Sylow | C29 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^28,g^c=g^28218 conjugacy classes — view the full character table.
| maximal subgroup of | #16821387, #16821389, D29×#442, … |
| maximal normal subgroup of | #16821387, #16821389, D29×#442, … |
| maximal quotient of | #16818315, #16818355, #16818405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 660);