Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #554 |
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^2681901 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #554×D269, C2×#31771309, #46824437, … |
| maximal normal subgroup of | #554×D269, C2×#31771309, #46824437, … |
| maximal quotient of | #46813757, #46813759, #46813783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1253);