Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#391 ⋊ C2 |
| Sylow | C13 ⋊ #2337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C13×#391 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C22×D52 | C22 |
| hypercenter | #391 | D13 |
| hypocenter | C13 | #2337 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #391 | |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^12,h^c=h^12,h^d=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2337, C2×#13117648, #16021841, … |
| maximal normal subgroup of | D13×#2337, C2×#13117648, #16021841, … |
| maximal quotient of | #15784192, #15784251, #15784257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7322);