Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C72 ⋊ #99 |
112 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^5,7^2|b^2=d,b^a=bc,d^a=de,f^a=f^6,c^b=ce,f^b=g^6,g^b=f^6,f^c=f^6,g^c=g^662 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 357);