Finite Group DatabasebetaFinite Group Databasebeta| order | 22912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C179 ⋊ #1319 |
134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,b^2=g,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^178,d^c=dg1984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22912, 2443);