Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D181⋊C32 |
| derived, Sylow | C181 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #10624382 |
| commutator, hypocenter | C181 | C2×C32 |
| Frattini | C8 | C2×#10624382 |
| Fitting | C16×C181 | C4 |
| socle | C2×C181 | C2×C16 |
| prime radical | C2×D181 | C16 |
| cosocle | #15668424 | C22 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^162,g^b=g^180,g^c=g^180784 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#10624382, #37548827, #37548870, … |
| maximal normal subgroup of | C32×#10624382, #37548827, #37548870, … |
| maximal quotient of | #37548826, #37548835, #37548879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1480);