Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C42×D257 |
| Fitting | C2×C42×C257 ⋊ C2 |
| derived, Sylow | C257 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D257 |
| commutator, hypocenter | C257 | C22×C42 |
| Frattini | C22 | C23×D257 |
| Fitting | C2×C42×C257 | C2 |
| socle | C23×C257 | C23 |
| prime radical | C23×D257 | C22 |
| cosocle | C22×C257 | C24 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8224 |
4160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D257, #45664012, #339×D257, … |
| maximal normal subgroup of | #336×D257, #45664012, #339×D257, … |
| maximal quotient of | C43×D257, C2×C42×Dic257, C2×#95×D257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 993);