Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C13 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D13 |
| commutator, socle | C2×C13 | C24×C4 |
| Fitting, prime radical | C13×#585 | C2 |
| cosocle | C4×C13 | C25 |
| hypercenter | #585 | D13 |
| hypocenter | C13 | #3573 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,h^a=h^12,e^b=eg,d^c=dg272 conjugacy classes — view the full character table.
| maximal subgroup of | #15868876, #15868882, #15868887, … |
| maximal normal subgroup of | #15868876, #15868882, #15868887, … |
| maximal quotient of | #16726340, #16726375, #16726556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19222);