Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | D13×#379 |
| Fitting | C13×#379 ⋊ C2 |
| Sylow | C13 ⋊ C2×#379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C13×#379 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C25×D13 | C2 |
| hypercenter | #379 | D13 |
| hypocenter | C13 | C2×#379 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #379 | |
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1304, #15753242, D13×#1316, … |
| maximal normal subgroup of | D13×#1304, #15753242, D13×#1316, … |
| maximal quotient of | D13×C22⋊#95, #15784124, Dic13×#379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6876);