Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #342 |
301 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 301 conjugacy classes of subgroups — too many to draw. Only its 64 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,b^2=c,b^a=bd,d^a=df,h^a=h^4,e^b=ef,g^b=g^2,g^c=g^488 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#64866, #72221747, #72221751, … |
| maximal normal subgroup of | D5×#64866, #72221747, #72221751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2187);