Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D42×D13 |
| Fitting | D42×C13 ⋊ C2 |
| Sylow | C13 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | D42×C13 | C2 |
| hypercenter | D42 | D13 |
| hypocenter | C13 | C2×D42 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ D42 | |
2536 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1619, D13×#1629, D13×#1639, … |
| maximal normal subgroup of | D13×#1619, D13×#1629, D13×#1639, … |
| maximal quotient of | D4×C22⋊C4×D13, D4×C4⋊C4×D13, D13×#2358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17945);