Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D4×#41×D79 |
| Fitting | D4×#41×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Frattini | C22 | C25×D79 |
| Fitting | D4×#41×C79 | C2 |
| hypercenter | D4×#41 | D79 |
| hypocenter | C79 | C2×D4×#41 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ D4×#41 | |
12314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
2050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1076521);