Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×(C2×D11)⋊C4 |
| Fitting | C2×C4×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14769478, #14769479, #14769486, … |
| maximal normal subgroup of | #14769478, #14769479, #14769486, … |
| maximal quotient of | C22⋊C4×(C2×D11)⋊C4, C4⋊C4×(C2×D11)⋊C4, D4×C11⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7327);