Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#1057 |
| derived, Sylow | C13 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #261 |
| commutator, hypocenter | C13 | C42×C8 |
| Frattini | C23 | C22×#261 |
| Fitting | C2×C42×C13 | C4 |
| socle, prime radical | C23×C13 | C22×C4 |
| cosocle | C22×Dic13 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C42 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #16776826, C4×C8×#1057, C4×#11718251, … |
| maximal normal subgroup of | #16776826, C4×C8×#1057, C4×#11718251, … |
| maximal quotient of | C4×C8×#1057, C4×#11718251, #97×#1057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20162);