Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | #95×D28 |
| Fitting | C4×C7×#95 ⋊ C2 |
| Sylow | C7 ⋊ D4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C22×C7 | C22×C42 |
| Fitting | C4×C7×#95 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C23×D28 | C22 |
| hypercenter | C4×#95 | D7 |
| hypocenter | C7 | D4×#95 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
3562 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 91039);