Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#10624382)⋊C8 |
| Fitting | C2×C8×C181 ⋊ C4 |
| Sylow | C181 ⋊ #336 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^162,g^e=g^180760 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#10624382)⋊C8, #37549383, #37549386, … |
| maximal normal subgroup of | C2×(C2×#10624382)⋊C8, #37549383, #37549386, … |
| maximal quotient of | #37548543, #37548544, #37548546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1414);