Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#261 |
| commutator, socle | C23×C13 | C22×C4 |
| Fitting | C22×Q8×C13 | C4 |
| prime radical, cosocle | C23×D13 | C23 |
| hypercenter | C22×Q8 | #261 |
| hypocenter | C13 | #1446 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
736 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=f,c^2=f,b^a=bd,c^a=ce,h^a=h^8,c^b=cf,h^g=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16777629, #16781447, #16781448, … |
| maximal normal subgroup of | #16777629, #16781447, #16781448, … |
| maximal quotient of | #16778229, #16786548, #16786549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19700);