Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#23777744 |
| Fitting | C22×C4⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#3544 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D79 |
| commutator, cosocle | C22×C79 | C26 |
| Frattini | C22 | C25×D79 |
| Fitting | C22×C4⋊Q8×C79 | C2 |
| socle | C23×C79 | C25 |
| hypercenter | C22×C4⋊Q8 | D79 |
| hypocenter | C79 | C2×#3544 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊Q8 | |
7086 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
2260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1077252);