Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C29 ⋊ C4 |
| Sylow | C29 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^12,c^b=cf,g^e=g^2892 conjugacy classes — view the full character table.
| maximal subgroup of | #16835447, #16835448, #16835451, … |
| maximal normal subgroup of | #16835447, #16835448, #16835451, … |
| maximal quotient of | #16835043, #16835044, #16835045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1560);