Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#13083443 |
| unambiguous semidirect product | D353⋊C42 |
| Fitting | C2×C4×C353 ⋊ C4 |
| derived, Sylow | C353 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
736 conjugacy classes — view the full character table.
| maximal subgroup of | #36378652, #36378657, #36378659, … |
| maximal normal subgroup of | #36378652, #36378657, #36378659, … |
| maximal quotient of | C42×#13083443, C2×(C2×#13083443)⋊C4, #36378723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 222);