Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C29×2−1+4 ⋊ C2 |
| Sylow | C29 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D29 |
| commutator, socle, cosocle | C2×C29 | C25 |
| Fitting | C29×2−1+4 | C2 |
| hypercenter | 2−1+4 | D29 |
| hypocenter | C29 | #585 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^28,g^d=g^28,g^e=g^28272 conjugacy classes — view the full character table.
| maximal subgroup of | #16828839, #16828844, #16828862, … |
| maximal normal subgroup of | #16828839, #16828844, #16828862, … |
| maximal quotient of | #16832692, #16832694, #16832698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1386);