Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ C2×#97 |
368 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 112 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=e,b^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^4,c^b=cf,h^b=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #72242206, #72242291 |
| maximal normal subgroup of | #72242206, #72242291 |
| maximal quotient of | #72242174 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3192);