Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2296 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C13×#385 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C24×C13 | C23 |
| hypercenter | #385 | D13 |
| hypocenter | C13 | #2296 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #385 | |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,d^2=f,b^a=be,c^a=cf,h^d=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15772092, #15772338, #15864003, … |
| maximal normal subgroup of | #15772092, #15772338, #15864003, … |
| maximal quotient of | #15784031, #15784046, #15784083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6989);