Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C82×C13 ⋊ C2 |
| Sylow | C13 ⋊ #1712 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #88128 |
| commutator, cosocle | C42×C13 | C23 |
| Frattini | C42 | C22×D13 |
| Fitting | C82×C13 | C2 |
| socle | C22×C13 | #127 |
| hypercenter | C82 | D13 |
| hypocenter | C13 | #1712 |
| LCS | G ▷ C42×C13 ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C82 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=df,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^12422 conjugacy classes — view the full character table.
| maximal subgroup of | #15749649, #15776314, #15777091, … |
| maximal normal subgroup of | #15749649, #15776314, #15777091, … |
| maximal quotient of | #15756700, #15762682, #15765688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4125);