Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #342 |
340 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=ce,b^a=bcd,d^a=df,g^a=g^2,h^a=h^3,c^b=cf,d^b=df,e^b=ef,g^b=h,h^b=g^4,g^c=g^4,h^c=h^446 conjugacy classes — view the full character table.
| maximal subgroup of | #72227920 |
| maximal normal subgroup of | #72227920 |
| maximal quotient of | #72227914 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2382);