Finite Group DatabasebetaFinite Group Databasebeta| order | 20812 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C43⋊#92150 |
| Fitting, socle, derived, Hall | C112×C43 ⋊ C4 |
| Sylow | C112 ⋊ Dic43 |
| Sylow | C43 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C43 | C4 |
| prime radical, cosocle | C43×C11⋊D11 | C2 |
| LCS | G ▷ C112×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 946 |
Polycyclic presentation:
2^2,11^2,43|a^2=b,c^a=c^8d^7,d^a=c^8d^3,e^a=e^42,c^b=c^10,d^b=d^101336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20812, 18);