Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C257 ⋊ C2 |
| Sylow | C257 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8224 |
Polycyclic presentation:
2^6,257|a^2=e,b^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^2561817 conjugacy classes. The character table is too large to display.
| maximal quotient of | #45667152, #45667154, #45667216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1212);