Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#340 ⋊ C2 |
| Sylow | C5 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D5×#102, C2×#10599573, #12097049, … |
| maximal normal subgroup of | C4×D5×#102, C2×#10599573, #12097049, … |
| maximal quotient of | #11989891, #11989921, #11989936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1655);