Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C42×D13 |
| Fitting | C22×C42×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D13 |
| commutator, hypocenter | C13 | C23×C42 |
| Frattini | C22 | C24×D13 |
| Fitting | C22×C42×C13 | C2 |
| socle | C24×C13 | C23 |
| prime radical | C24×D13 | C22 |
| cosocle | C22×C13 | C25 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15768135, #15768159, C4×D13×#95, … |
| maximal normal subgroup of | #15768135, #15768159, C4×D13×#95, … |
| maximal quotient of | C2×C43×D13, C22×C42×Dic13, C22×D13×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17664);