Finite Group DatabasebetaFinite Group Databasebeta| order | 11744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D367)⋊C4 |
| Fitting | C22⋊C4×C367 ⋊ C2 |
| Sylow | C367 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,367|a^2=e,c^2=e,b^a=bd,f^c=f^3661850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×D367, C2×(C22⋊D367)⋊C4, C4×#19154576, … |
| maximal normal subgroup of | C4×D4×D367, C2×(C22⋊D367)⋊C4, C4×#19154576, … |
| maximal quotient of | #37554033, C22⋊C4×Dic367, #37554037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11744, 106);