Finite Group DatabasebetaFinite Group Databasebeta| order | 11632 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D727)⋊C4 |
| Fitting | C2×C4×C727 ⋊ C2 |
| Sylow | C727 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,727|a^2=d,b^a=bc,e^b=e^7262914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D727, C2×(C2×D727)⋊C4, #37551505, … |
| maximal normal subgroup of | C22⋊C4×D727, C2×(C2×D727)⋊C4, #37551505, … |
| maximal quotient of | C727⋊#95, (C2×D727)⋊C8, #37551462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11632, 17);