Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C29×#97 ⋊ C2 |
| Sylow | C29 ⋊ #496 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D116 |
| commutator, cosocle | C2×C4×C29 | C23 |
| Frattini | C2×C4 | C22×D29 |
| Fitting | C29×#97 | C2 |
| socle | C22×C29 | C2×D4 |
| hypercenter | #97 | D29 |
| hypocenter | C29 | #496 |
| LCS | G ▷ C2×C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^28,c^b=cf296 conjugacy classes — view the full character table.
| maximal subgroup of | #16818782, #16818786, #16818787, … |
| maximal normal subgroup of | #16818782, #16818786, #16818787, … |
| maximal quotient of | #16819114, #16819120, #16819131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 938);