Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1808 |
Polycyclic presentation:
2^5,113|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^112574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 123);