Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3×C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C112 ⋊ C4×C5 |
| Hall | C32×#10597245 ⋊ C4 |
| Hall | C11⋊(C11⋊#157) ⋊ C5 |
| Hall | #10597245 ⋊ #157 |
| Sylow | C112 ⋊ C5×#157 |
| Sylow | C32 ⋊ #14559052 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C112 | C4×C5 |
| prime radical | C3⋊D3×#10597245 | C2 |
| cosocle | C112×C3⋊D3 | C2×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3^2,11^2|a^2=c,d^a=de,e^a=de^2,f^a=f^10,g^a=g^10,f^b=f^4,g^b=g^3,d^c=d^2,e^c=e^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 425);