Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C7 |
No aliases for this group.
| Fitting | C72×M16 ⋊ C2 |
| Sylow | C72 ⋊ #100 |
230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
2^5,7^2|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^6,g^a=g^6,d^b=de251 conjugacy classes — view the full character table.
| maximal subgroup of | #100×C7⋊D7, #72246212, #72246215, … |
| maximal normal subgroup of | #100×C7⋊D7, #72246212, #72246215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 307);