Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ C4×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C13×#389 | C2 |
| socle, prime radical, cosocle | C23×C13 | C24 |
| hypercenter | #389 | D13 |
| hypocenter | C13 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #389 | |
588 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,c^2=f,d^2=eg,b^a=be,c^a=cf,h^b=h^12,h^d=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15750895, #15750977, #15750990, … |
| maximal normal subgroup of | #15750895, #15750977, #15750990, … |
| maximal quotient of | #15784109, #15784111, Dic13×#389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7081);