Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ #529 |
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|c^2=e,d^2=f,b^a=bf,d^a=de,g^a=g^10188 conjugacy classes — view the full character table.
| maximal subgroup of | #13067022, #13067025, #13067027, … |
| maximal normal subgroup of | #13067022, #13067025, #13067027, … |
| maximal quotient of | #13071014, #13071059, #13071080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 929);