Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| derived, Hall | C5×C112⋊C9 ⋊ C4 |
| Hall | C112⋊C9 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ Dic9 |
| Sylow | C112 ⋊ C9⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #17983714 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C5×C112⋊C9 | C4 |
| Frattini | C3 | #20300038 |
| Fitting, socle | C3×C5×C112 | Dic3 |
| prime radical | C3×C5⋊(C11⋊D11) | D3 |
| cosocle | C5⋊((C11⋊D11)⋊C9) | C2 |
| LCS | G ▷ C5×C112⋊C9 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11^2,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^5f^7,f^a=ef^6,g^a=g^2,d^b=d^4,e^b=e^10,f^b=f^10,e^c=e^3f,f^c=e^9f^7171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 218);