Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#261 |
| commutator, socle | C2×C13 | C23×C8 |
| Fitting | C13×#131 | C4 |
| prime radical | #41×D13 | C4 |
| cosocle | #1055 | C24 |
| hypercenter | #131 | #261 |
| hypocenter | C13 | #3407 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ #131 | |
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 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=e,e^2=f,f^2=g,d^a=dg,h^a=h^8,c^b=cg,h^d=h^12,h^e=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #16789401, #16789402, #16790559, … |
| maximal normal subgroup of | #16789401, #16789402, #16790559, … |
| maximal quotient of | #16806730, #16806741, #16806742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21478);