Finite Group DatabasebetaFinite Group Databasebeta| order | 37568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C587 ⋊ C2 |
| Sylow | C587 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4696 |
Polycyclic presentation:
2^6,587|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^586,d^b=df,e^b=ef,d^c=df4997 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37568, 717);