Finite Group DatabasebetaFinite Group Databasebeta| order | 846 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D47 |
| unambiguous semidirect product | C47⋊(C2×C32) |
| Fitting, socle, Hall | C32×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D47 |
| commutator, cosocle, hypocenter | C47 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 423 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D47, C3⋊D3×D47, C2×C32×D47, … |
| maximal normal subgroup of | C3×D3×D47, C3⋊D3×D47, C2×C32×D47, … |
| maximal quotient of | C32×Dic47, C2×C32×D47, C32×C5×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(846, 5);