Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#66937 |
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#66937, #14759800, #14759810, … |
| maximal normal subgroup of | C8×#66937, #14759800, #14759810, … |
| maximal quotient of | C4×#10622569, C4×#10622278, C4×#10622564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7021);