Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C29 ⋊ #391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D29 |
| commutator | C22×C29 | C22×C4 |
| Fitting | C2×C42×C29 | C2 |
| socle, prime radical, cosocle | C23×C29 | C23 |
| hypercenter | C2×C42 | D29 |
| hypocenter | C29 | #391 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^28476 conjugacy classes — view the full character table.
| maximal subgroup of | #16817317, #16819452, #16819708, … |
| maximal normal subgroup of | #16817317, #16819452, #16819708, … |
| maximal quotient of | #16817722, #16817725, #16817746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 455);