Finite Group DatabasebetaFinite Group Databasebeta| order | 37568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #107×C587 ⋊ C2 |
| Sylow | C587 ⋊ C4×D8 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18784 |
Polycyclic presentation:
2^6,587|a^2=e,c^2=e,d^2=f,b^a=bd,d^a=df,d^b=df,g^b=g^586,g^c=g^5864130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37568, 631);