Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D13⋊C64 |
| derived, Sylow | C13 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #261 |
| commutator, hypocenter | C13 | C2×C64 |
| Frattini | C16 | C2×#261 |
| Fitting | C13×C32 | C4 |
| socle | C2×C13 | C2×C32 |
| prime radical | C2×D13 | C32 |
| cosocle | #88034 | C22 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^8,h^b=h^12,h^c=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #261×C64, #16778138, #16778203, … |
| maximal normal subgroup of | #261×C64, #16778138, #16778203, … |
| maximal quotient of | #16778137, #16778146, #16778212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19678);