Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4×C5 |
| direct product | C22⋊C4×#1044 |
| Fitting | C52×C22⋊C4 ⋊ C4 |
| Sylow | C52 ⋊ C4×C22⋊C4 |
648 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72221640, #120×#1044, #72221664, … |
| maximal normal subgroup of | #72221640, #120×#1044, #72221664, … |
| maximal quotient of | #72221257, #72221259, #104×#1044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7188);