Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C11⋊(C11⋊#4380) |
| Fitting, socle, derived, Hall | C32×C5×C112 ⋊ C4 |
| Hall | C32×C112 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ #157 |
| Sylow | C112 ⋊ #4380 |
| Hall | C32×C5 ⋊ C11⋊Dic11 |
| Sylow | C32 ⋊ C11⋊(C11⋊AGL(1,𝔽5)) |
| Sylow | C5 ⋊ C11⋊(C11⋊#157) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C112 | C4 |
| prime radical, cosocle | C112×C3⋊D15 | C2 |
| LCS | G ▷ C32×C5×C112 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,11^2|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^10,g^a=g^10,c^b=c^2,d^b=d^2,e^b=e^41455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 632);