Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#11719648 |
| Fitting | C22×C13×#41 ⋊ C2 |
| Sylow | C13 ⋊ C2×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D13 |
| commutator, cosocle | C2×C13 | C26 |
| Frattini | C2 | C25×D13 |
| Fitting | C22×C13×#41 | C2 |
| socle | C22×C13 | C25 |
| hypercenter | C22×#41 | D13 |
| hypocenter | C13 | C2×#585 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
5956 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15862170, #15862171, #15862172, … |
| maximal normal subgroup of | #15862170, #15862171, #15862172, … |
| maximal quotient of | C2×#13128035, C2×#13128037, C2×#13128039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19318);