Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×C4⋊C8 ⋊ C2 |
| Sylow | C52 ⋊ D4⋊C8 |
328 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|b^2=c,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^4,h^a=h^4,d^b=df268 conjugacy classes — view the full character table.
| maximal subgroup of | #72253065, #72253071, C5⋊D5×D4⋊C8 |
| maximal normal subgroup of | #72253065, #72253071, C5⋊D5×D4⋊C8 |
| maximal quotient of | #72253079 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1867);