Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C29×H(5,𝔽2) ⋊ C2 |
| Sylow | C29 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D29 |
| commutator, socle, cosocle | C2×C29 | C25 |
| Fitting | C29×H(5,𝔽2) | C2 |
| hypercenter | H(5,𝔽2) | D29 |
| hypocenter | C29 | #585 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
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^e=g^28272 conjugacy classes — view the full character table.
| maximal subgroup of | #16828837, #16828842, #16828860, … |
| maximal normal subgroup of | #16828837, #16828842, #16828860, … |
| maximal quotient of | #16832690, #16832692, #16832696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1384);