Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D29⋊#131 |
| Sylow | C29 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,e^2=f,g^a=g^12,c^b=cf,g^d=g^28,g^e=g^28110 conjugacy classes — view the full character table.
| maximal subgroup of | #16835268, #16835272, #16835531, … |
| maximal normal subgroup of | #16835268, #16835272, #16835531, … |
| maximal quotient of | #16836052, C4×#11745346, C4×#11745348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1625);