Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5 |
No aliases for this group.
| Fitting | C52×#117 ⋊ C2 |
| Sylow | C52 ⋊ C4×#41 |
1240 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 335 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=f,d^2=e,c^a=cf,g^a=g^4,h^a=h^4,d^c=df280 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#41×C5⋊D5, #72221194, #72223414, … |
| maximal normal subgroup of | C4×#41×C5⋊D5, #72221194, #72223414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9405);