Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C11×Q16 ⋊ C2 |
| Sylow | C11 ⋊ #495 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=ef,c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^10,c^b=cef,e^c=ef92 conjugacy classes — view the full character table.
| maximal subgroup of | #13070673, #13070674, #13070680, … |
| maximal normal subgroup of | #13070673, #13070674, #13070680, … |
| maximal quotient of | #13068209, #13068210, #13068219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 723);