Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C22×D7×2−1+4 |
| Fitting | C22×C7×2−1+4 ⋊ C2 |
| Sylow | C7 ⋊ C23×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D7 |
| commutator, cosocle | C2×C7 | C27 |
| Frattini | C2 | C26×D7 |
| Fitting | C22×C7×2−1+4 | C2 |
| socle | C23×C7 | C25 |
| hypercenter | C22×2−1+4 | D7 |
| hypocenter | C7 | C23×2−1+4 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C22×2−1+4 | |
59806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083456);