Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C5×C11×D11 |
| Fitting, socle | C2×C32×C5×C112 ⋊ C2 |
| derived | C11 ⋊ C22×C32×C5×C11 |
| Hall | C32×C5×C112 ⋊ C22 |
| Hall | C32×C112 ⋊ C22×C5 |
| Hall | C5×C112 ⋊ C22×C32 |
| Sylow | C112 ⋊ C22×C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5×C11 | D11 |
| commutator, cosocle, hypocenter | C11 | C22×C32×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C112 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C32×C5×C11 | |
360 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
6930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 723);