Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C72 ⋊ #137 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^5,7^2|a^2=e,b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^6,c^b=cde,d^b=de,g^b=g^6,d^c=de98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 549);