Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D13⋊C32 |
| unambiguous semidirect product | D13⋊(C2×C32) |
| derived, Sylow | C13 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #261 |
| commutator, hypocenter | C13 | C22×C32 |
| Frattini | C8 | C22×#261 |
| Fitting | C2×C13×C16 | C4 |
| socle | C22×C13 | C2×C16 |
| prime radical | C22×D13 | C16 |
| cosocle | #6090 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#261)⋊C32, #16778004, #16778005, … |
| maximal normal subgroup of | (C2×#261)⋊C32, #16778004, #16778005, … |
| maximal quotient of | C4×D13⋊C32, C2×#13129941, D13⋊(C22⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20929);