Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D363⋊D15 |
| Fitting, derived, Hall | C32×C5×C121 ⋊ C22 |
| Hall | C32×C121 ⋊ C2×D5 |
| Hall | C5×C121 ⋊ D32 |
| Sylow | C121 ⋊ D3×D15 |
| Hall | C32×C5 ⋊ C2×D121 |
| Sylow | C32 ⋊ D5×D121 |
| Sylow | C5 ⋊ (C3⋊D3)⋊D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C5×C121 | C22 |
| Frattini | C11 | D33⋊D15 |
| socle | C32×C5×C11 | C2×D11 |
| LCS | G ▷ C32×C5×C121 | |
| UCS | C1 | |
132 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 132 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:
2^2,3^2,5,11^2|f^11=g^10,c^a=c^2,e^a=e^4,f^a=f^10g,g^a=g^10,c^b=c^2,d^b=d^2,e^b=e^41467 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 103);