Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#13063703 |
| unambiguous semidirect product | D349⋊C42 |
| Fitting | C2×C4×C349 ⋊ C4 |
| derived, Sylow | C349 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
728 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#13063703)⋊C8, #36375014, #36375016, … |
| maximal normal subgroup of | (C2×#13063703)⋊C8, #36375014, #36375016, … |
| maximal quotient of | C42×#13063703, C2×(C2×#13063703)⋊C4, #36375080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 222);