Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#22575415 |
| Fitting | C2×C4⋊C4×C269 ⋊ C2 |
| Sylow | C269 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809202, #46809222, #46810676, … |
| maximal normal subgroup of | #46809202, #46809222, #46810676, … |
| maximal quotient of | C2×#31770452, C2×C4⋊C4×Dic269, C4×#22575415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1009);