Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#384 ⋊ C2 |
| Sylow | C13 ⋊ #2441 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#384 | C2 |
| prime radical | C23×D13 | C23 |
| hypercenter | #384 | D13 |
| hypocenter | C13 | #2441 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #384 | |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=cg,h^b=h^12,h^c=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | #15920024, #15920027, #15920069, … |
| maximal normal subgroup of | #15920024, #15920027, #15920069, … |
| maximal quotient of | #15784892, #15785572, #15785859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 8226);