Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#13083443 |
| unambiguous semidirect product | D353⋊(C4⋊C4) |
| Fitting | C2×C4×C353 ⋊ C4 |
| Sylow | C353 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
724 conjugacy classes — view the full character table.
| maximal subgroup of | #36378660, #36378661, #36378666, … |
| maximal normal subgroup of | #36378660, #36378661, #36378666, … |
| maximal quotient of | C2×(C2×#13083443)⋊C4, C4×C4⋊#13083443, #36378729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 224);