Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×C4⋊C4×D11 |
| Fitting | C4×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×#1279, #14643307, #14643343, … |
| maximal normal subgroup of | D11×#1279, #14643307, #14643343, … |
| maximal quotient of | C4×D11×#95, C4×#10622262, C4×C4⋊C4×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6843);