Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#127 ⋊ C2 |
| Sylow | C11 ⋊ #453 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #66990 |
| commutator, cosocle | C2×C4×C11 | C23 |
| Frattini | C2×C4 | C22×D11 |
| Fitting | C11×#127 | C2 |
| socle | C2×C11 | #120 |
| hypercenter | #127 | D11 |
| hypocenter | C11 | #453 |
| LCS | G ▷ C2×C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #127 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^6,11|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 | #13066760, #13066762, #13070600, … |
| maximal normal subgroup of | #13066760, #13066762, #13070600, … |
| maximal quotient of | #13067533, #13067538, #13067560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 609);