Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D11 |
| commutator | C2×C11 | C23×C4 |
| Fitting, prime radical | C22×D4×C11 | C2 |
| socle, cosocle | C22×C11 | C24 |
| hypercenter | C22×D4 | D11 |
| hypocenter | C11 | #518 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=e,d^a=df,g^a=g^10,c^b=cf134 conjugacy classes — view the full character table.
| maximal subgroup of | #13068722, #13068725, #13068825, … |
| maximal normal subgroup of | #13068722, #13068725, #13068825, … |
| maximal quotient of | #13070969, #13070973, #13070977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1248);