Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C13×#124 ⋊ C2 |
| Sylow | C13 ⋊ #2858 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C2×C13×#124 | C2 |
| prime radical | C2×#88194 | C2 |
| hypercenter | C2×#124 | D13 |
| hypocenter | C13 | #2858 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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|b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^c=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15761921, #15761939, #15916335, … |
| maximal normal subgroup of | #15761921, #15761939, #15916335, … |
| maximal quotient of | #15794109, #15794185, #15794259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12865);