Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#10622570 |
| Fitting | C22×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C2×#390 |
1360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14652595, #14652613, C4×#10622570, … |
| maximal normal subgroup of | #14652595, #14652613, C4×#10622570, … |
| maximal quotient of | C2×Dic11⋊#95, C2×#13066852, C2×#13066853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6964);