Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C22×C16×D13 |
| Fitting | C22×C13×C16 ⋊ C2 |
| derived, Sylow | C13 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D13 |
| commutator, hypocenter | C13 | C23×C16 |
| Frattini | C8 | C23×D13 |
| Fitting | C22×C13×C16 | C2 |
| socle | C23×C13 | C2×C8 |
| prime radical | C23×D13 | C8 |
| cosocle | C8×C13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C16 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×#1374, #15777760, D13×#1379, … |
| maximal normal subgroup of | D13×#1374, #15777760, D13×#1379, … |
| maximal quotient of | C2×C4×C16×D13, C22×C16×Dic13, C2×D13×C22⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17602);