Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D13×#564 |
| Fitting | C13×#564 ⋊ C2 |
| Sylow | C13 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C13×#564 | C2 |
| prime radical | C22×D13 | C24 |
| hypercenter | #564 | D13 |
| hypocenter | C13 | C2×#564 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1658, D13×#1663, #15844219, … |
| maximal normal subgroup of | D13×#1658, D13×#1663, #15844219, … |
| maximal quotient of | D13×#2382, #16025639, Dic13×#564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18652);