Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C2×C13×#125 | C2 |
| socle, prime radical, cosocle | C23×C13 | C24 |
| hypercenter | C2×#125 | D13 |
| hypocenter | C13 | #2382 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
408 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^12,c^b=cef,d^b=de206 conjugacy classes — view the full character table.
| maximal subgroup of | #15757285, #15757289, #15757292, … |
| maximal normal subgroup of | #15757285, #15757289, #15757292, … |
| maximal quotient of | #15784543, #15784564, #15784569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7696);