Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#22551588 |
| Fitting | C22×D4×C257 ⋊ C2 |
| Sylow | C257 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D257 |
| commutator, cosocle | C22×C257 | C24 |
| Frattini | C22 | C23×D257 |
| Fitting | C22×D4×C257 | C2 |
| socle | C23×C257 | C23 |
| hypercenter | C22×D4 | D257 |
| hypocenter | C257 | C2×#127 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8224 |
2588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45664715, #45664716, #45664718, … |
| maximal normal subgroup of | #45664715, #45664716, #45664718, … |
| maximal quotient of | C2×#30656606, C2×#30656637, C2×#30656638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1088);