Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×#261 |
| unambiguous semidirect product | D13⋊(C24×C4) |
| Fitting, socle | C25×C13 ⋊ C4 |
| derived, Sylow | C13 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #261 |
| commutator, hypocenter | C13 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C13 | C4 |
| prime radical | C25×D13 | C2 |
| cosocle | D13 | C26 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C25 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13130009, #261×#379, #16792539, … |
| maximal normal subgroup of | C2×#13130009, #261×#379, #16792539, … |
| maximal quotient of | C24×C4×#261, C24×C22⋊#261, C24×C4⋊#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21507);