Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#66927 |
| Fitting | C2×C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D11 |
| commutator, cosocle | C22×C11 | C24 |
| Frattini | C22 | C23×D11 |
| Fitting | C2×C42×C11 | C2 |
| socle | C23×C11 | C23 |
| hypercenter | C2×C42 | D11 |
| hypocenter | C11 | C2×#127 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10622123, #13067283, #13067285, … |
| maximal normal subgroup of | C2×#10622123, #13067283, #13067285, … |
| maximal quotient of | C2×#10622548, C2×#10622552, C4×#66927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 925);