Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D13×C32 |
| Fitting | C2×C13×C32 ⋊ C2 |
| derived, Sylow | C13 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D13 |
| commutator, hypocenter | C13 | C22×C32 |
| Frattini | C16 | C22×D13 |
| Fitting | C2×C13×C32 | C2 |
| socle | C22×C13 | C2×C16 |
| prime radical | C22×D13 | C16 |
| cosocle | C13×C16 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15750727, C4×D13×C32, D13×#1397, … |
| maximal normal subgroup of | #15750727, C4×D13×C32, D13×#1397, … |
| maximal quotient of | C4×D13×C32, C2×C32×Dic13, D13×C22⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6798);