Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42×C5 |
No aliases for this group.
| Fitting | C42×C52 ⋊ C4 |
| Sylow | C52 ⋊ #376 |
464 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=e,c^a=cf,g^a=g^3,h^a=h^2,g^d=g^4,h^d=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #72221487, #72221539, #72221541, … |
| maximal normal subgroup of | #72221487, #72221539, #72221541, … |
| maximal quotient of | C2×#13104824 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7176);