Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×D8 ⋊ C4 |
| Sylow | C52 ⋊ #357 |
208 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 32 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,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^3,h^a=h^2,d^b=de,e^b=ef,g^c=g^4,h^c=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #72220697, #72220775, #72220776, … |
| maximal normal subgroup of | #72220697, #72220775, #72220776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2726);