Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D724 |
| Fitting | C4×Q8×C181 ⋊ C2 |
| Sylow | C181 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D181 |
| commutator, socle, cosocle | C22×C181 | C24 |
| Fitting | C4×Q8×C181 | C2 |
| prime radical | C2×D724 | C22 |
| hypercenter | C4×Q8 | D181 |
| hypocenter | C181 | D4×Q8 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
1825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37532822, #37532826, #37532884, … |
| maximal normal subgroup of | #37532822, #37532826, #37532884, … |
| maximal quotient of | Q8×#15668426, C4⋊C4×D724, Q8×C4⋊Dic181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1216);