Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #95×C257 ⋊ C2 |
| Sylow | C257 ⋊ #397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D257 |
| commutator, socle, cosocle | C23×C257 | C23 |
| Fitting | #95×C257 | C2 |
| prime radical | C23×D257 | C22 |
| hypercenter | #95 | D257 |
| hypocenter | C257 | #397 |
| LCS | G ▷ C23×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ #95 | |
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^256,g^c=g^2562582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45663307, #45663312, #45663335, … |
| maximal normal subgroup of | #45663307, #45663312, #45663335, … |
| maximal quotient of | #45662566, #45662568, #45662577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 476);