Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#15668452 |
| derived, Sylow | C181 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10624382 |
| commutator, hypocenter | C181 | C22×C16 |
| Frattini | C4 | C22×#10624382 |
| Fitting | C22×C4×C181 | C4 |
| socle, prime radical | C23×C181 | C8 |
| cosocle | #13089678 | C23 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | #37548759, #37548760, #37548775, … |
| maximal normal subgroup of | #37548759, #37548760, #37548775, … |
| maximal quotient of | C2×C4×#15668452, C2×C22⋊#15668452, C2×C4⋊#15668452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1602);