Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C13×#585 ⋊ C2 |
| Sylow | C13 ⋊ #3025 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #88207 |
| commutator, cosocle | C23×C13 | C24 |
| Frattini | C23 | C23×D13 |
| Fitting | C13×#585 | C2 |
| socle | C2×C13 | C2×#120 |
| hypercenter | #585 | D13 |
| hypocenter | C13 | #3025 |
| LCS | G ▷ C23×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #585 | |
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|d^2=g,b^a=be,c^a=cf,h^a=h^12,f^b=fg,e^c=eg236 conjugacy classes — view the full character table.
| maximal subgroup of | #15780204, #15780210, #15780211, … |
| maximal normal subgroup of | #15780204, #15780210, #15780211, … |
| maximal quotient of | #15835188, #15835197, #15835206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13902);