Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #456 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=f,c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^10,d^b=df,e^b=ef,e^c=ef101 conjugacy classes — view the full character table.
| maximal subgroup of | #13070635, #13070636, #13070640, … |
| maximal normal subgroup of | #13070635, #13070636, #13070640, … |
| maximal quotient of | #13067579, #13067585, #13067590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 778);