Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C25 ⋊ C4 |
| Sylow | C25 ⋊ #386 |
429 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 75 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=d,g^5=h,c^a=cf,g^a=g^2h,h^a=h^2,c^b=ce,g^d=g^4h^4,h^d=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #120×#1035, #72275645, #72275687, … |
| maximal normal subgroup of | #120×#1035, #72275645, #72275687, … |
| maximal quotient of | #72275686, #72275692, #72275697 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1120);