Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C7×C43 ⋊ C32×C4 |
| Hall | ΓL(1,𝔽8)×C43⋊C3 ⋊ C4 |
| Hall | Dic301 ⋊ C32 |
| Sylow | C43 ⋊ C3×ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ C3×(C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)⋊(D43⋊C3) |
| commutator, hypocenter | C7×C43 | C32×C4 |
| Fitting, socle, cosocle | C2×C7×C43 | C2×C32 |
| prime radical | C2×ΓL(1,𝔽8)×C43⋊C3 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,43,2|a^2=f,d^a=d^6,e^a=e^42,e^b=e^36,d^c=d^2112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 85);