Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C52 ⋊ C4×M16 |
311 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 82 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=d,b^2=e,d^2=f,e^2=f,c^a=cf,h^a=h^2,c^b=cf,g^b=g^2,h^d=h^4,g^e=g^464 conjugacy classes — view the full character table.
| maximal subgroup of | #72221499, #72221503, #72221578, … |
| maximal normal subgroup of | #72221499, #72221503, #72221578, … |
| maximal quotient of | #72220679, C2×#13107464, #72221645, … |
| holomorph of | #170 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9816);