Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C163 ⋊ #2276 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D163 |
| commutator | C2×C163 | C22×C42 |
| Fitting | #376×C163 | C2 |
| socle, prime radical, cosocle | C23×C163 | C24 |
| hypercenter | #376 | D163 |
| hypocenter | C163 | #2276 |
| LCS | G ▷ C2×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #376 | |
628 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20864 |
Polycyclic presentation:
2^7,163|a^2=f,b^2=g,c^2=ef,d^2=e,b^a=be,d^a=de,c^b=ce,h^d=h^1623308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 6873);