Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C52×C22⋊C4 ⋊ C22 |
| Sylow | C52 ⋊ B(4,𝔽2) |
526 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^6,5^2|c^2=def,c^a=ce,d^a=df,g^a=g^4,c^b=cd,e^b=ef,h^b=h^4,d^c=df,e^c=ef100 conjugacy classes — view the full character table.
| maximal subgroup of | #72213486, #72226502, #72226506, … |
| maximal normal subgroup of | #72213486, #72226502, #72226506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2943);