Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2845 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C24 |
| Fitting | C13×#382 | C2 |
| hypercenter | #382 | D13 |
| hypocenter | C13 | #2845 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #382 | |
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=ef,b^2=g,c^2=eg,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^12194 conjugacy classes — view the full character table.
| maximal subgroup of | #15765997, #15765998, #15766000, … |
| maximal normal subgroup of | #15765997, #15765998, #15766000, … |
| maximal quotient of | #15793742, #15793744, #15793746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12785);