Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×C7×H(5,𝔽2) ⋊ C2 |
| Sylow | C7 ⋊ #32898 |
4360 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 319 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|b^a=be,c^a=cf,d^a=dg,i^a=i^6,f^b=fh,e^c=eh253 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#32898, #72277880 |
| maximal normal subgroup of | D7×#32898, #72277880 |
| maximal quotient of | #72260047 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 318339);