Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×Dic269 |
| Sylow | C269 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×Dic269, #103×Dic269, #46810717, … |
| maximal normal subgroup of | #101×Dic269, #103×Dic269, #46810717, … |
| maximal quotient of | C2×C4⋊C4×Dic269, C4×Q8×Dic269, C2×#31770491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1015);