Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C83×#1312 ⋊ C2 |
| Sylow | C83 ⋊ #11402 |
322 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|a^2=d,b^2=e,d^2=f,e^2=g,g^2=h,b^a=bf,c^b=ch,i^c=i^823392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 78560);