Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | Dic7×#391 |
| Sylow | C7 ⋊ C4×#391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C22×C7 | C22×C42 |
| Fitting | C2×C7×#391 | C2 |
| socle, prime radical, cosocle | C24×C7 | C24 |
| hypercenter | C2×#391 | D7 |
| hypocenter | C7 | C4×#391 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#391 | |
2110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1792 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 90771);