Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting | C72×Q16 ⋊ C2 |
| Sylow | C72 ⋊ SD32 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
Polycyclic presentation:
2^5,7^2|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^6,g^a=g^6,c^b=cd,d^b=de179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 312);