Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D4×C25 ⋊ C2 |
| Sylow | C25 ⋊ #539 |
327 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|c^2=e,g^5=h,b^a=bf,d^a=de,g^a=g^4h^4,h^a=h^4,d^b=df,d^c=df262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1239);