Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D13×#519 |
| Fitting | C13×#519 ⋊ C2 |
| Sylow | C13 ⋊ C2×#519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator | C2×C13 | C24×C4 |
| Fitting | C13×#519 | C2 |
| socle, cosocle | C22×C13 | C25 |
| prime radical | C23×D13 | C23 |
| hypercenter | #519 | D13 |
| hypocenter | C13 | C2×#519 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×#1830, D13×#1857, #15863744, … |
| maximal normal subgroup of | D13×#1830, D13×#1857, #15863744, … |
| maximal quotient of | D13×#2274, D13×#2276, #16021166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17698);