Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4⋊Q8×C257 ⋊ C2 |
| Sylow | C257 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D257 |
| commutator, socle, cosocle | C22×C257 | C24 |
| Fitting | C4⋊Q8×C257 | C2 |
| prime radical | C2×D1028 | C22 |
| hypercenter | C4⋊Q8 | D257 |
| hypocenter | C257 | D4×Q8 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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,b^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^256,g^d=g^2561817 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45663420, #45663424, #45663482, … |
| maximal normal subgroup of | #45663420, #45663424, #45663482, … |
| maximal quotient of | #45667154, #45667220, #45667221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1214);