Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D99⋊D55 |
| Fitting, derived, Hall | C5×C9×C112 ⋊ C22 |
| Hall | C9×C112 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×D9 |
| Sylow | C112 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ D112 |
| Sylow | C9 ⋊ D11×D55 |
| Sylow | C5 ⋊ D99⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C112 | C22 |
| Frattini | C3 | D33⋊D55 |
| socle | C3×C5×C112 | C2×D3 |
| LCS | G ▷ C5×C9×C112 | |
| UCS | C1 | |
180 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,3,5,11^2,3|c^3=g^2,d^a=d^4,e^a=e^10,f^a=f^10,c^b=c^2g,f^b=f^10,g^b=g^21419 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 297);