Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=d,c^2=de,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 | #16835075, #16835077, #16835079, … |
| maximal normal subgroup of | #16835075, #16835077, #16835079, … |
| maximal quotient of | C4⋊C4×#6599, #16835284, #16835546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1598);