Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1843 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D13 |
| commutator, socle, prime radical | C23×C13 | C22×C4 |
| Fitting | C13×#376 | C2 |
| cosocle | C22×C4×C13 | C23 |
| hypercenter | #376 | D13 |
| hypocenter | C13 | #1843 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^12,c^b=cg284 conjugacy classes — view the full character table.
| maximal subgroup of | #15757038, #15757039, #15766988, … |
| maximal normal subgroup of | #15757038, #15757039, #15766988, … |
| maximal quotient of | #15756672, #15756675, #15756679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4664);