Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C52 ⋊ C4 |
| Sylow | C52 ⋊ #339 |
440 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 78 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:
2^6,5^2|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,e^a=ef,g^a=g^2,h^a=h^2,g^c=g^4,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #72221210, #104×#1043, #72221214, … |
| maximal normal subgroup of | #72221210, #104×#1043, #72221214, … |
| maximal quotient of | C2×#13100240, #72253133 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2592);