Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C52×C4⋊C4 ⋊ C22 |
| Sylow | C52 ⋊ C2×#102 |
496 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|c^2=d,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=ce,e^b=ef,h^b=h^4,e^c=ef124 conjugacy classes — view the full character table.
| maximal subgroup of | #72220757, #72220787, #72220796, … |
| maximal normal subgroup of | #72220757, #72220787, #72220796, … |
| maximal quotient of | #72220701 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3126);