Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×C8×D13 |
| Fitting | C2×C4×C8×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C22×C4×C8 |
760 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×#1273, #15752299, #15752303, … |
| maximal normal subgroup of | D13×#1273, #15752299, #15752303, … |
| maximal quotient of | C2×C82×D13, C2×D13×#322, C8×M16×D13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12909);