Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D257 |
| Fitting | C4×Q8×C257 ⋊ C2 |
| Sylow | C257 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8224 |
2600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D257, #45662713, #45662747, … |
| maximal normal subgroup of | Q8⋊C8×D257, #45662713, #45662747, … |
| maximal quotient of | C4×C4⋊C4×D257, C4×#22551557, C4×Q8×Dic257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1012);