Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#64859 |
| Sylow | C52 ⋊ #346 |
123 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72242231, C5×#10598515, #72242277, … |
| maximal normal subgroup of | #72242231, C5×#10598515, #72242277, … |
| maximal quotient of | C5×#10598537 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2400);