Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2371 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C13×#376 | C2 |
| socle, prime radical, cosocle | C23×C13 | C24 |
| hypercenter | #376 | D13 |
| hypocenter | C13 | #2371 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #376 | |
448 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 185 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=g,c^2=e,d^2=f,b^a=be,c^a=cf,d^b=de,h^b=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15760540, #15760542, #15760550, … |
| maximal normal subgroup of | #15760540, #15760542, #15760550, … |
| maximal quotient of | #15784371, #15784434, #15784439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7615);