Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2966 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting | C13×#126 | C4 |
| prime radical | #88138 | C4 |
| cosocle | C2×Dic13 | C24 |
| hypercenter | #126 | #261 |
| hypocenter | C13 | #2966 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #126 | |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^5,h^b=h^12,h^c=h^8,h^d=h^12,h^f=h^1298 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊#2966, C2×#13131654, #16808506, … |
| maximal normal subgroup of | D13⋊#2966, C2×#13131654, #16808506, … |
| maximal quotient of | #16797286, #16797287, #16797297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21328);