Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C29 ⋊ C2 |
| Sylow | C29 ⋊ #520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D29 |
| commutator | C2×C29 | C23×C4 |
| Fitting | C4×Q8×C29 | C2 |
| socle, cosocle | C22×C29 | C24 |
| prime radical | C2×#90809 | C2 |
| hypercenter | C4×Q8 | D29 |
| hypocenter | C29 | #520 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^28,g^c=g^28,g^d=g^28314 conjugacy classes — view the full character table.
| maximal subgroup of | #16828319, #16828323, #16828330, … |
| maximal normal subgroup of | #16828319, #16828323, #16828330, … |
| maximal quotient of | #16821846, #16821852, #16821857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1031);