Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D11 |
| commutator, socle, cosocle | C23×C11 | C23 |
| Fitting | C22×Q8×C11 | C2 |
| prime radical | C23×D11 | C22 |
| hypercenter | C22×Q8 | D11 |
| hypocenter | C11 | #393 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=f,c^2=f,b^a=be,c^a=cd,g^a=g^10,c^b=cf122 conjugacy classes — view the full character table.
| maximal subgroup of | #13067566, #13067571, #13067593, … |
| maximal normal subgroup of | #13067566, #13067571, #13067593, … |
| maximal quotient of | #13066858, #13066875, #13066887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 763);