Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1181 |
| commutator, socle | C22×C29 | C22×C4 |
| Fitting, prime radical | C2×D4×C29 | C4 |
| cosocle | C2×Dic29 | C23 |
| hypercenter | C2×D4 | #1181 |
| hypocenter | C29 | #436 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^17,c^b=cf,g^c=g^12,g^e=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | #16835093, #16835094, #16835101, … |
| maximal normal subgroup of | #16835093, #16835094, #16835101, … |
| maximal quotient of | #16835125, #16835128, #16835132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1584);