Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽5) ⋊ C22⋊C4 |
151 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|b^2=c,b^a=bd,f^a=f^4,g^a=g^4,e^b=e^4,g^b=g^4,f^e=fg74 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 112);