Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ #2313 |
512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=g,b^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^80,c^b=ce,h^g=h^172904 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20987);