Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×C4⋊Q8 ⋊ C4 |
| Sylow | C13 ⋊ #2331 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting | C13×C4⋊Q8 | C4 |
| prime radical, cosocle | C22×D13 | C24 |
| hypercenter | C4⋊Q8 | #261 |
| hypocenter | C13 | #2331 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
460 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 170 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|a^2=g,b^2=fg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^5,c^b=ce,h^b=h^8,h^g=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | #16783683, #16783684, #16783685, … |
| maximal normal subgroup of | #16783683, #16783684, #16783685, … |
| maximal quotient of | #16791570, #16791581, #16791600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21005);