Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
| direct product | Q8×#6455 |
| Fitting | C7×Q8×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ Q8×#117 |
2434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 328993);