Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, derived, Hall | C9×C112 ⋊ C22×C5 |
| Hall | C9×#10597243 ⋊ C22 |
| Hall | D99⋊D11 ⋊ C5 |
| Hall | #10597243 ⋊ C2×D9 |
| Sylow | C112 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ #11925892⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C22×C5 |
| Frattini | C3 | #20300008 |
| socle | C3×C112 | C2×C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,3,11^2,3|d^3=g^2,d^a=d^2g,e^a=e^10,g^a=g^2,e^b=e^10,f^b=f^10,e^c=e^4,f^c=f^4117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 188);