Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#14559049) |
| derived, Hall | C32×#10597245 ⋊ C4 |
| Hall | C32×C112 ⋊ Dic5 |
| Hall | #10597245 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C3⋊Dic15 |
| Sylow | C32 ⋊ #14559049 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊#11925890) |
| commutator, hypocenter | C32×#10597245 | C4 |
| Fitting, socle | C2×C32×C112 | D5 |
| prime radical, cosocle | C2×C32×#10597245 | C2 |
| LCS | G ▷ C32×#10597245 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,11^2,2|a^2=g,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^3f^3,f^a=ef^8,e^d=e^4f^8,f^d=f^3294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 359);