Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic617 |
| Sylow | C617 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D617 |
| commutator | C2×C617 | C22×C4 |
| Fitting | C2×Q8×C617 | C2 |
| socle, prime radical, cosocle | C22×C617 | C23 |
| hypercenter | C2×Q8 | D617 |
| hypocenter | C617 | C4×Q8 |
| LCS | G ▷ C2×C617 ▷ C617 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19744 |
3100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 113);