Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C13×#563 ⋊ C2 |
| Sylow | C13 ⋊ #3545 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C13×#563 | C2 |
| hypercenter | #563 | D13 |
| hypocenter | C13 | #3545 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #563 | |
1060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|c^2=fg,d^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^12,c^b=cg,d^b=df,h^b=h^12,h^c=h^12,h^e=h^12152 conjugacy classes — view the full character table.
| maximal subgroup of | #15844716, #15844724, #15844755, … |
| maximal normal subgroup of | #15844716, #15844724, #15844755, … |
| maximal quotient of | #16025749, #16026042, #16026320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18868);