Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×H(5,𝔽2) ⋊ C2 |
| Sylow | C11 ⋊ #577 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|b^2=f,c^2=f,d^2=f,e^2=f,d^a=de,e^a=ef,g^a=g^10,c^b=cf,e^d=ef107 conjugacy classes — view the full character table.
| maximal subgroup of | #13080377, #13080380, #13080389, … |
| maximal normal subgroup of | #13080377, #13080380, #13080389, … |
| maximal quotient of | #13077142, #13077146, #13077209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1286);