Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#13063703 |
| unambiguous semidirect product | D349⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#13063703)⋊C22 |
| Fitting | C23×C349 ⋊ C4 |
| Sylow | C349 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
716 conjugacy classes — view the full character table.
| maximal subgroup of | #36375021, #36375022, C4×C22⋊#13063703, … |
| maximal normal subgroup of | #36375021, #36375022, C4×C22⋊#13063703, … |
| maximal quotient of | C2×(C2×#13063703)⋊C4, C4×C22⋊#13063703, #36375085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 223);