Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#89804 |
| Fitting | C4×C7×#120 ⋊ C2 |
| Sylow | C7 ⋊ C4×B(4,𝔽2) |
1910 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 175548);