Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #120×C541 ⋊ C2 |
| Sylow | C541 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^6,541|b^a=bd,c^a=ce,e^b=ef,d^c=df,g^c=g^5403796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 735);