Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C13×#41 ⋊ C2 |
| Sylow | C13 ⋊ #3481 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C4×C13×#41 | C2 |
| hypercenter | C4×#41 | D13 |
| hypocenter | C13 | #3481 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|e^2=fg,b^a=bf,c^a=cg,h^a=h^12,d^b=df,h^c=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15754967, #15754968, #15829886, … |
| maximal normal subgroup of | #15754967, #15754968, #15829886, … |
| maximal quotient of | #16022361, #16022371, #16022384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18120);