Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
| direct product | M128×D79 |
| Fitting | C79×M128 ⋊ C2 |
| Sylow | C79 ⋊ C2×M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C22×D79 |
| commutator, socle | C2×C79 | C22×C32 |
| Fitting | C79×M128 | C2 |
| prime radical | C22×D79 | C32 |
| cosocle | C32×C79 | C23 |
| hypercenter | M128 | D79 |
| hypocenter | C79 | C2×M128 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C32 ◁ M128 | |
134 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5056 |
3280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90603);