Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2968 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting | C13×#125 | C4 |
| prime radical | #88149 | C4 |
| cosocle | C2×Dic13 | C24 |
| hypercenter | #125 | #261 |
| hypocenter | C13 | #2968 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #125 | |
372 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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,h^a=h^5,h^b=h^12,d^c=dg,h^c=h^8,h^f=h^1292 conjugacy classes — view the full character table.
| maximal subgroup of | #16783988, #16783990, #16783992, … |
| maximal normal subgroup of | #16783988, #16783990, #16783992, … |
| maximal quotient of | #16797308, #16797326, #16797383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21339);