Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D11 |
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13068538, #13068549, D11×#391, … |
| maximal normal subgroup of | #13068538, #13068549, D11×#391, … |
| maximal quotient of | C22×C4⋊C4×D11, C2×C4×Q8×D11, C22×#66940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1366);