Finite Group DatabasebetaFinite Group Databasebeta| order | 30848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C241 ⋊ #2225 |
130 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30848 |
Polycyclic presentation:
2^7,241|a^2=d,b^2=d,c^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^240,e^c=ef,f^c=fg,h^c=h^2402669 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30848, 6651);