Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C11⋊Dic55)⋊C9 |
| derived, Hall | C5×C112 ⋊ C4×C9 |
| Hall | C5×C112⋊C9 ⋊ C4 |
| Hall | C11⋊Dic55 ⋊ C9 |
| Hall | C112⋊C9 ⋊ Dic5 |
| Sylow | C112 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ (C11⋊Dic11)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊((C11⋊D11)⋊C3) |
| commutator, hypocenter | C5×C112 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C112 | C2×C3 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C2×C3 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,11^2,2,3|a^2=f,b^3=g,c^a=c^4,d^a=d^10,e^a=e^10,d^b=d^7e^5,e^b=d^4e^3672 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 152);