Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#15667734 |
| Fitting | C4×C353 ⋊ C8 |
| Sylow | C353 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|a^2=d,b^2=c,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 | D4⋊#15667734, Q8⋊#15667734, #36378876, … |
| maximal normal subgroup of | D4⋊#15667734, Q8⋊#15667734, #36378876, … |
| maximal quotient of | #36378876, #36378877, (C2×#15667734)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 239);