Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×D29 |
| Fitting | C29×2−1+4 ⋊ C2 |
| Sylow | C29 ⋊ C2×2−1+4 |
| 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 | C2×2−1+4 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×#454, D29×#456, #16828853, … |
| maximal normal subgroup of | D29×#454, D29×#456, #16828853, … |
| maximal quotient of | D29×#519, D29×#520, #16832701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1381);