Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #340 |
241 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 58 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=c,b^2=d,d^2=f,e^2=f,b^a=be,d^a=df,e^a=ef,h^a=h^2,g^b=g^2,h^c=h^4,g^d=g^458 conjugacy classes — view the full character table.
| maximal subgroup of | #72221512, #72221634, #72221635 |
| maximal normal subgroup of | #72221512, #72221634, #72221635 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5613);