Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C353 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5648 |
Polycyclic presentation:
2^6,353|a^2=e,e^2=f,b^a=bd,g^a=g^311,g^c=g^352,g^e=g^3521448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 1517);