Finite Group DatabasebetaFinite Group Databasebeta| order | 30848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#101×C241 ⋊ C2 |
| Sylow | C241 ⋊ #2005 |
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^7,241|b^2=g,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^240,c^b=cf,d^b=dg,h^b=h^240,d^c=dg2666 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30848, 5548);