Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#67040 |
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D11 |
| commutator, cosocle | C2×C11 | C25 |
| Frattini | C2 | C24×D11 |
| Fitting | C22×Q8×C11 | C2 |
| socle | C22×C11 | C24 |
| hypercenter | C22×Q8 | D11 |
| hypocenter | C11 | C2×2−1+4 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #13068574, #13068577, #13068588, … |
| maximal normal subgroup of | #13068574, #13068577, #13068588, … |
| maximal quotient of | C2×#10623103, C2×#10623343, C2×#10623035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1368);