Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C113 ⋊ C2 |
| Sylow | C113 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 904 |
Polycyclic presentation:
2^5,113|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^112,d^b=de,f^b=f^112571 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 174);