Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D11 |
| commutator, socle, prime radical, cosocle | C22×C11 | C24 |
| Fitting | C4×Q8×C11 | C2 |
| hypercenter | C4×Q8 | D11 |
| hypocenter | C11 | #557 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=e,b^2=f,c^2=f,d^2=ef,d^a=def,g^a=g^10,c^b=cf125 conjugacy classes — view the full character table.
| maximal subgroup of | #13067711, #13067715, #13067773, … |
| maximal normal subgroup of | #13067711, #13067715, #13067773, … |
| maximal quotient of | Q8×C4⋊Dic11, #13071534, #13071571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1020);