Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5 |
No aliases for this group.
| Sylow | C52 ⋊ C2×#131 |
696 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=e,c^2=f,e^2=f,g^a=g^3,h^a=h^2,d^b=df,g^e=g^4,h^e=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #72221086, #72221227, #72221229, … |
| maximal normal subgroup of | #72221086, #72221227, #72221229, … |
| maximal quotient of | C2×#13107772, #72242672 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10124);