Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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|a^2=e,c^2=e,e^2=f,b^a=bd,g^a=g^17,g^c=g^12,g^e=g^28110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14272190, D4×D29⋊C8, #16836206, … |
| maximal normal subgroup of | C2×#14272190, D4×D29⋊C8, #16836206, … |
| maximal quotient of | #16835072, #16835075, #16835076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1576);