Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #87831 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#87832 |
| Sylow | C52 ⋊ C4×C4⋊C4 |
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11717375, #72221110, C4×#11717356, … |
| maximal normal subgroup of | C4×#11717375, #72221110, C4×#11717356, … |
| maximal quotient of | #72220765, #72223423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6349);