Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D11 |
| commutator, socle, prime radical | C22×C11 | C22×C4 |
| Fitting | C4×Q8×C11 | C2 |
| cosocle | C2×C4×C11 | C23 |
| hypercenter | C4×Q8 | D11 |
| hypocenter | C11 | #446 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=d,b^2=e,c^2=e,d^2=f,c^a=cf,g^a=g^10,c^b=ce128 conjugacy classes — view the full character table.
| maximal subgroup of | #13067453, #13067455, #13067467, … |
| maximal normal subgroup of | #13067453, #13067455, #13067467, … |
| maximal quotient of | #13068485, #13068491, #13069175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 556);