Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C257 ⋊ #382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D257 |
| commutator | C22×C257 | C22×C4 |
| Fitting | #95×C257 | C2 |
| socle, prime radical, cosocle | C23×C257 | C23 |
| hypercenter | #95 | D257 |
| hypocenter | C257 | #382 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ #95 | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16448 |
Polycyclic presentation:
2^6,257|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^c=g^2562588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45662855, #45662857, #45662878, … |
| maximal normal subgroup of | #45662855, #45662857, #45662878, … |
| maximal quotient of | #45662544, #45662545, #45662548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 413);