Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C52×C8 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×M16 |
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,c^2=e,e^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=cf,g^b=g^4,g^d=g^4,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | M16×D5⋊AGL(1,𝔽5), #72220841, #72220842, … |
| maximal normal subgroup of | M16×D5⋊AGL(1,𝔽5), #72220841, #72220842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6196);