Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D11 |
| commutator, socle | C2×C11 | C22×C8 |
| Fitting | C11×#131 | C2 |
| prime radical | C11×#41 | C4 |
| cosocle | C8×C11 | C23 |
| hypercenter | #131 | D11 |
| hypocenter | C11 | #504 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C8 ◁ #131 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=d,d^2=e,e^2=f,g^a=g^10,c^b=cf140 conjugacy classes — view the full character table.
| maximal subgroup of | #13070450, #13070453, #13070455, … |
| maximal normal subgroup of | #13070450, #13070453, #13070455, … |
| maximal quotient of | #13070213, #13070230, #13070375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 672);