Finite Group DatabasebetaFinite Group Databasebeta| order | 32896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #356×C257 ⋊ C2 |
| Sylow | C257 ⋊ #2132 |
250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4112 |
Polycyclic presentation:
2^7,257|a^2=e,c^2=g,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,d^b=dg,e^b=efg,h^b=h^256,h^c=h^256,e^d=eg1690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32896, 6194);