Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C433 ⋊ #413 |
150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^6,433|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^179,e^b=ef,g^e=g^4321750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1535);