Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C42×C29 ⋊ C2 |
| Sylow | C29 ⋊ #529 |
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^28476 conjugacy classes — view the full character table.
| maximal subgroup of | #16817898, #16817901, #16817903, … |
| maximal normal subgroup of | #16817898, #16817901, #16817903, … |
| maximal quotient of | #16821890, #16821935, #16821956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1083);