Finite Group DatabasebetaFinite Group Databasebeta| order | 22912 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #349×C179 ⋊ C2 |
| Sylow | C179 ⋊ #2115 |
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5728 |
Polycyclic presentation:
2^7,179|a^2=e,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,e^b=eg,h^c=h^1782002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22912, 6129);