Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#1181 |
| unambiguous semidirect product | D29⋊(C23×C4) |
| Fitting, socle | C24×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #1181 |
| commutator, hypocenter | C29 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C29 | C4 |
| prime radical | C24×D29 | C2 |
| cosocle | D29 | C25 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C24 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1630);