Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C72 ⋊ #104 |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^5,7^2|b^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^6,d^b=de,f^b=f^6146 conjugacy classes — view the full character table.
| maximal subgroup of | #72214778, #72214827, #72214884, … |
| maximal normal subgroup of | #72214778, #72214827, #72214884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 226);