Finite Group DatabasebetaFinite Group Databasebeta| order | 20636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic67⋊C11) |
| unambiguous semidirect product | (C67⋊C11)⋊Dic7 |
| unambiguous semidirect product | Dic469⋊C11 |
| derived, Hall | C7×C67 ⋊ C4×C11 |
| Hall | C7×C67⋊C11 ⋊ C4 |
| Hall | Dic469 ⋊ C11 |
| Hall | C67⋊C11 ⋊ Dic7 |
| Sylow | C67 ⋊ C11×Dic7 |
| Sylow | C7 ⋊ Dic67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(D67⋊C11) |
| commutator, hypocenter | C7×C67 | C4×C11 |
| Fitting, socle, cosocle | C2×C7×C67 | C2×C11 |
| prime radical | C2×C7×C67⋊C11 | C2 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1876 |
Polycyclic presentation:
2,7,11,67,2|a^2=e,b^a=b^6,d^a=d^66,d^c=d^64152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20636, 12);