Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C4×C29 ⋊ C4 |
| Sylow | C29 ⋊ #380 |
234 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=d,b^a=bd,c^a=ce,g^a=g^12,g^f=g^28140 conjugacy classes — view the full character table.
| maximal subgroup of | #16834354, #16834355, #16834366, … |
| maximal normal subgroup of | #16834354, #16834355, #16834366, … |
| maximal quotient of | #16834666, #16834668, #16834670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1491);