Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D7×#1357 |
| Fitting | C7×#1357 ⋊ C2 |
| Sylow | C7 ⋊ C2×#1357 |
494 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
115 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#11992, D7×#12310, D7×#12366 |
| maximal normal subgroup of | D7×#11992, D7×#12310, D7×#12366 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 80770);