Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C13×#519 ⋊ C2 |
| Sylow | C13 ⋊ #3486 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C13×#519 | C2 |
| hypercenter | #519 | D13 |
| hypocenter | C13 | #3486 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^12,d^b=df,h^c=h^12248 conjugacy classes — view the full character table.
| maximal subgroup of | #15872094, #15894362, #15894493, … |
| maximal normal subgroup of | #15872094, #15894362, #15894493, … |
| maximal quotient of | #16022942, #16023203, #16023858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18162);