Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D632 |
| Fitting | C24×C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C24×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | D316 |
| commutator, cosocle | C4×C79 | C26 |
| Frattini | C4 | C25×D79 |
| Fitting | C24×C8×C79 | C2 |
| socle | C25×C79 | D4 |
| hypercenter | C24×C8 | D79 |
| hypocenter | C79 | C24×D8 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C25 ◁ C24×C4 ◁ C24×C8 | |
15454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
5104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1083343);