Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C163 ⋊ #2854 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D163 |
| commutator, socle, cosocle | C23×C163 | C24 |
| Fitting, prime radical | C2×#121×C163 | C2 |
| hypercenter | C2×#121 | D163 |
| hypocenter | C163 | #2854 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
688 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10432 |
Polycyclic presentation:
2^7,163|b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dg,h^d=h^1622312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 12836);