Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #391×C173 ⋊ C2 |
| Sylow | C173 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=g,b^2=f,c^2=e,d^2=g,b^a=be,c^a=cf,h^b=h^172,h^c=h^172,h^d=h^1722464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 7053);