Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2792 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C24 |
| Fitting | C13×#387 | C2 |
| hypercenter | #387 | D13 |
| hypocenter | C13 | #2792 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #387 | |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=efg,b^2=e,c^2=f,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^12,c^b=cg,d^b=de200 conjugacy classes — view the full character table.
| maximal subgroup of | #16070584, #16070597, #16070601, … |
| maximal normal subgroup of | #16070584, #16070597, #16070601, … |
| maximal quotient of | #15790906, #15790910, #15791469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12309);