Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×#3937 |
| Fitting | C2×C42×C52 ⋊ C2 |
| Sylow | C52 ⋊ C2×#104 |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13100574, C2×C5×#65366, C2×#13100579, … |
| maximal normal subgroup of | C2×#13100574, C2×C5×#65366, C2×#13100579, … |
| maximal quotient of | C5×D3×#3937 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4550);