Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C3⋊(C3⋊#14559075) |
| Fitting, socle, Hall | C32×C112 ⋊ Dic5 |
| derived, Hall | C32×#10597245 ⋊ C4 |
| Hall | #10597245 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C3⋊Dic15 |
| Sylow | C32 ⋊ #14559075 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C32×#10597245 | C4 |
| Fitting, socle | C32×C112 | Dic5 |
| prime radical, cosocle | C32×#11925893 | C2 |
| LCS | G ▷ C32×#10597245 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^6g^6,g^a=f^3g^5,f^b=f^10,g^b=g^10,f^e=f^9g^3,g^e=g^5102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 499);