Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic903 |
| unambiguous semidirect product | C7⋊(C3⋊Dic129) |
| unambiguous semidirect product | C43⋊(C3⋊Dic21) |
| derived, Hall | C32×C7×C43 ⋊ C4 |
| Hall | C32×C43 ⋊ Dic7 |
| Hall | C7×C43 ⋊ C3⋊Dic3 |
| Hall | C32×C7 ⋊ Dic43 |
| Sylow | C43 ⋊ C3⋊Dic21 |
| Sylow | C32 ⋊ Dic301 |
| Sylow | C7 ⋊ C3⋊Dic129 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D903 |
| commutator, hypocenter | C32×C7×C43 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C7×C43 | C2 |
| LCS | G ▷ C32×C7×C43 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,43,2|a^2=f,b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^422712 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 137);