Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×3−1+2×C127 ⋊ C3 |
| Sylow | C127 ⋊ C9⋊H(3,𝔽3) |
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10287 |
Polycyclic presentation:
3^5,127|b^3=d,b^a=bd,c^a=ce,f^c=f^1071437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 183);