Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D13 |
| commutator, socle, prime radical | C23×C13 | C22×C4 |
| Fitting | C13×#336 | C2 |
| cosocle | C22×C4×C13 | C23 |
| hypercenter | #336 | D13 |
| hypocenter | C13 | #1917 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^12,c^b=cg,h^b=h^12,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1917, C2×#13115403, #15864981, … |
| maximal normal subgroup of | D13×#1917, C2×#13115403, #15864981, … |
| maximal quotient of | #15761067, #15761074, #15761081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5077);