Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C22×D13⋊C16 |
| unambiguous semidirect product | D13⋊(C22×C16) |
| derived, Sylow | C13 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #261 |
| commutator, hypocenter | C13 | C23×C16 |
| Frattini | C4 | C23×#261 |
| Fitting | C22×C8×C13 | C4 |
| socle | C23×C13 | C2×C8 |
| prime radical | C23×D13 | C8 |
| cosocle | #1055 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C8 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#261)⋊C16, #16789041, #16789049, … |
| maximal normal subgroup of | C2×(C2×#261)⋊C16, #16789041, #16789049, … |
| maximal quotient of | C2×C4×D13⋊C16, C22×#11718257, C2×D13⋊(C22⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21470);