Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D13×#576 |
| Fitting | C13×#576 ⋊ C2 |
| Sylow | C13 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D13 |
| commutator, cosocle | C4×C13 | C25 |
| Frattini | C4 | C24×D13 |
| Fitting | C13×#576 | C2 |
| socle | C2×C13 | C23×D4 |
| hypercenter | #576 | D13 |
| hypocenter | C13 | C2×#576 |
| LCS | G ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #576 | |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2192, D13×#2194, #16016881, … |
| maximal normal subgroup of | D13×#2192, D13×#2194, #16016881, … |
| maximal quotient of | D13×#2897, D13×#2913, D13×#2946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19258);