Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ #3523 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | D4×Q8×C13 | C2 |
| prime radical | #88193 | C22 |
| hypercenter | D4×Q8 | D13 |
| hypocenter | C13 | #3523 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^e=h^12194 conjugacy classes — view the full character table.
| maximal subgroup of | #16745495, #16745499, #16745558, … |
| maximal normal subgroup of | #16745495, #16745499, #16745558, … |
| maximal quotient of | #16023151, #16023658, #16023774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18597);