Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C29 ⋊ C4 |
| Sylow | C29 ⋊ #518 |
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^6,29|a^2=f,b^a=be,d^a=de,g^a=g^12,c^b=ce,g^f=g^28104 conjugacy classes — view the full character table.
| maximal subgroup of | #16835447, #16835463, #16835497, … |
| maximal normal subgroup of | #16835447, #16835463, #16835497, … |
| maximal quotient of | #16835928, #16835930, #16835931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1616);