Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D13 |
| commutator, socle | C2×C13 | C22×C16 |
| Fitting | C13×#504 | C2 |
| prime radical | C13×#41 | C8 |
| cosocle | C13×C16 | C23 |
| hypercenter | #504 | D13 |
| hypocenter | C13 | #2258 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C16 ◁ #504 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^12,c^b=cg320 conjugacy classes — view the full character table.
| maximal subgroup of | #15783480, #15783483, #15783485, … |
| maximal normal subgroup of | #15783480, #15783483, #15783485, … |
| maximal quotient of | #15783099, #15783116, #15783405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6804);