Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C42×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×#117 |
768 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|c^2=f,d^2=e,d^a=df,g^a=g^4,d^b=df,h^b=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #72221487, #72221489, #72221490, … |
| maximal normal subgroup of | #72221487, #72221489, #72221490, … |
| maximal quotient of | C2×#13105083 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7435);