Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C25 ⋊ C4 |
| Sylow | C25 ⋊ #518 |
507 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 155 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=e,g^5=h,d^a=df,g^a=g^2h,h^a=h^2,c^b=cf,g^e=g^4h^4,h^e=h^494 conjugacy classes — view the full character table.
| maximal subgroup of | H(5,𝔽2)×#1035, #72275692, #72275694, … |
| maximal normal subgroup of | H(5,𝔽2)×#1035, #72275692, #72275694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2022);