Finite Group DatabasebetaFinite Group Databasebeta| order | 20512 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D641 |
| Fitting | C2×D4×C641 ⋊ C2 |
| Sylow | C641 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D641 |
| commutator, cosocle | C2×C641 | C24 |
| Frattini | C2 | C23×D641 |
| Fitting | C2×D4×C641 | C2 |
| socle | C22×C641 | C23 |
| hypercenter | C2×D4 | D641 |
| hypocenter | C641 | C22×D4 |
| LCS | G ▷ C2×C641 ▷ C641 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5128 |
3220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20512, 182);