Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×D13⋊C8 |
| unambiguous semidirect product | D13⋊(C23×C8) |
| derived, Sylow | C13 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #261 |
| commutator, hypocenter | C13 | C24×C8 |
| Frattini | C2 | C24×#261 |
| Fitting | C23×C4×C13 | C4 |
| socle | C24×C13 | C2×C4 |
| prime radical | C24×D13 | C4 |
| cosocle | Dic13 | C25 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #16785256, #16785259, #16785280, … |
| maximal normal subgroup of | #16785256, #16785259, #16785280, … |
| maximal quotient of | C23×C4×#1057, C22×C4×D13⋊C8, C22×D13⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21494);