Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2413 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#386 | C2 |
| prime radical | C22×D4×C13 | C22 |
| hypercenter | #386 | D13 |
| hypocenter | C13 | #2413 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #386 | |
610 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=cg,h^b=h^12,h^c=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | #15900288, #15900295, #15916089, … |
| maximal normal subgroup of | #15900288, #15900295, #15916089, … |
| maximal quotient of | #15784809, #15785654, #15785749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7920);