Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D13×#577 |
| Fitting | C13×#577 ⋊ C2 |
| Sylow | C13 ⋊ C2×#577 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D13 |
| commutator, cosocle | C4×C13 | C25 |
| Frattini | C4 | C24×D13 |
| Fitting | C13×#577 | C2 |
| socle | C2×C13 | C23×D4 |
| hypercenter | #577 | D13 |
| hypocenter | C13 | C2×#577 |
| LCS | G ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #577 | |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3288, D13×#3289, D13×#3290, … |
| maximal normal subgroup of | D13×#3288, D13×#3289, D13×#3290, … |
| maximal quotient of | D13×#2897, D13×#2898, D13×#2912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19264);