Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D353⋊M16 |
| Sylow | C353 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|a^2=d,d^2=e,b^a=be,f^a=f^311,f^c=f^352,f^d=f^352724 conjugacy classes — view the full character table.
| maximal subgroup of | #36378654, #36378656, #36378658, … |
| maximal normal subgroup of | #36378654, #36378656, #36378658, … |
| maximal quotient of | #36378746, C4×#19150746, C4×#19150747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 231);