Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C72 ⋊ #137 |
147 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 40 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:
2^5,7^2|c^2=e,d^2=e,b^a=be,f^a=f^6,c^b=cd,d^b=de,g^b=g^6,d^c=de107 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 550);