Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C13 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#261 |
| commutator, socle | C2×C13 | C24×C4 |
| Fitting | C13×2−1+4 | C4 |
| prime radical | #11719652 | C2 |
| cosocle | Dic13 | C25 |
| hypercenter | 2−1+4 | #261 |
| hypocenter | C13 | #3573 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,h^a=h^8,e^b=eg,d^c=dg,h^c=h^12,h^d=h^12,h^f=h^12119 conjugacy classes — view the full character table.
| maximal subgroup of | #16799818, #16799820, #16799822, … |
| maximal normal subgroup of | #16799818, #16799820, #16799822, … |
| maximal quotient of | #16808027, #16808028, #16808058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21506);