Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4×C5 |
No aliases for this group.
| Fitting | C52×#97 ⋊ C2 |
| Sylow | C52 ⋊ C4×M16 |
568 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=e,b^2=e,c^2=d,d^2=f,g^a=g^4,h^a=h^4,c^b=cf280 conjugacy classes — view the full character table.
| maximal subgroup of | C4×M16×C5⋊D5, #72220973, #72221172, … |
| maximal normal subgroup of | C4×M16×C5⋊D5, #72220973, #72221172, … |
| maximal quotient of | #72221036 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4916);