Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of (((C5⋊D5)⋊C5)⋊C2)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽5) ⋊ C4⋊C4 |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,b^a=bc,e^a=e^2,f^a=f^3g^3,e^b=f^4g,f^b=e^4g^4,g^b=g^4,e^c=e^4,f^c=f^4g^2,f^e=fg44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 271);