Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C7 |
No aliases for this group.
| Fitting | C72×SD16 ⋊ C2 |
| Sylow | C72 ⋊ AGL(1,ℤ/8) |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
2^5,7^2|c^2=e,d^2=e,c^a=ce,f^a=f^6,g^a=g^6,c^b=cd,d^b=de,d^c=de179 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×C7⋊D7, #72245150, #72245202, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×C7⋊D7, #72245150, #72245202, … |
| maximal quotient of | #72259368, C2×#13096554, #72259560 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 720);