Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×M32 ⋊ C2 |
| Sylow | C52 ⋊ #509 |
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|c^2=def,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^4,h^a=h^4,c^b=cf256 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#509, #72253097, #72253104, … |
| maximal normal subgroup of | C5⋊D5×#509, #72253097, #72253104, … |
| maximal quotient of | #72242287, C2×#13102771 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5123);