Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ #518 |
752 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 161 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=e,c^2=f,d^a=df,g^a=g^2,h^a=h^2,c^b=cf,g^b=g^4,g^e=g^4,h^e=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #72220926, #72220956, #72220979, … |
| maximal normal subgroup of | #72220926, #72220956, #72220979, … |
| maximal quotient of | #72253324, #72253337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9915);