Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#261 |
| commutator, socle | C2×C13 | C22×C16 |
| Fitting | C13×M32 | C4 |
| prime radical | #6127 | C8 |
| cosocle | #6090 | C23 |
| hypercenter | M32 | #261 |
| hypocenter | C13 | #2258 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ M32 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^8,c^b=cg,h^b=h^12,h^d=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | #16791465, #16791466, #16791468, … |
| maximal normal subgroup of | #16791465, #16791466, #16791468, … |
| maximal quotient of | #16791147, #16791148, #16791168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20934);