Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D269 |
| Fitting | C22×Q8×C269 ⋊ C2 |
| Sylow | C269 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810807, #46810818, #391×D269, … |
| maximal normal subgroup of | #46810807, #46810818, #391×D269, … |
| maximal quotient of | C22×C4⋊C4×D269, C2×C4×Q8×D269, C22×#22575418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1372);