Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#124 ⋊ C2 |
| Sylow | C11 ⋊ #455 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|c^2=f,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^10,c^b=ce,d^b=df,d^c=df86 conjugacy classes — view the full character table.
| maximal subgroup of | #13066763, #13066765, #13070606, … |
| maximal normal subgroup of | #13066763, #13066765, #13070606, … |
| maximal quotient of | #13067567, #13067572, #13067594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 593);