Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C8 · Schur multiplier (H2) = C215 |
| direct product | C24×C8×D79 |
| Fitting | C24×C8×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C25×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C8 | D79 |
| commutator, hypocenter | C79 | C25×C8 |
| Frattini | C4 | C25×D79 |
| Fitting | C24×C8×C79 | C2 |
| socle | C25×C79 | C2×C4 |
| prime radical | C25×D79 | C4 |
| cosocle | C4×C79 | C26 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C24×C8 | |
15454 conjugacy classes of subgroups; only the 8715 normal subgroups are shown.
This group has 15454 conjugacy classes of subgroups — too many to draw. Only its 8715 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10112 |
5248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1083321);