Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#15667734 |
| unambiguous semidirect product | (C2×#15667734)⋊C2 |
| Fitting | C22×C353 ⋊ C8 |
| Sylow | C353 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|a^2=d,d^2=e,b^a=bc,f^a=f^283,f^d=f^311,f^e=f^352196 conjugacy classes — view the full character table.
| maximal subgroup of | #36378872, #36378873, C2×C22⋊#15667734, … |
| maximal normal subgroup of | #36378872, #36378873, C2×C22⋊#15667734, … |
| maximal quotient of | #36378872, #36378873, D4⋊#15667734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 238);