Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×#261 |
| unambiguous semidirect product | D13⋊(C22×C42) |
| Fitting | C23×C4×C13 ⋊ C4 |
| derived, Sylow | C13 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #261 |
| commutator, hypocenter | C13 | C23×C42 |
| Frattini | C2 | C24×#261 |
| Fitting | C23×C4×C13 | C4 |
| socle | C24×C13 | C2×C4 |
| prime radical | C24×D13 | C22 |
| cosocle | C2×D13 | C25 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C4 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#261)⋊#95, #16785250, #16785274, … |
| maximal normal subgroup of | (C2×#261)⋊#95, #16785250, #16785274, … |
| maximal quotient of | C22×C42×#261, C23×(C2×#261)⋊C4, C22×#11719057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21480);