Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Fitting | C52×C4⋊C8 ⋊ C2 |
| Sylow | C52 ⋊ C8×D4 |
536 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 157 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=e,c^2=d,d^2=f,b^a=be,g^a=g^4,h^a=h^4,c^b=ce280 conjugacy classes — view the full character table.
| maximal subgroup of | #72253065, C8×D4×C5⋊D5, #72253073 |
| maximal normal subgroup of | #72253065, C8×D4×C5⋊D5, #72253073 |
| maximal quotient of | #72253065 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5052);