Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C29 ⋊ C4 |
| Sylow | C29 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=e,d^2=f,c^b=cf,g^b=g^12,g^e=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | #16834541, #16834544, #16834545, … |
| maximal normal subgroup of | #16834541, #16834544, #16834545, … |
| maximal quotient of | C8×#90800, C8×#90796, #16834695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1512);