Finite Group DatabasebetaFinite Group Databasebeta| order | 29824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #323×C233 ⋊ C2 |
| Sylow | C233 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7456 |
Polycyclic presentation:
2^7,233|a^2=e,c^2=g,e^2=g,b^a=bd,d^a=df,e^b=ef,h^c=h^2322596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29824, 2825);