Finite Group DatabasebetaFinite Group Databasebeta| order | 11564 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C49) |
| derived, Sylow | C59 ⋊ C4×C49 |
| Hall | C49×C59 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D59 |
| commutator, hypocenter | C59 | C4×C49 |
| Frattini | C2×C7 | C7×D59 |
| Fitting | C2×C49×C59 | C2 |
| socle, prime radical, cosocle | C2×C7×C59 | C2×C7 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C49 | |
18 conjugacy classes of subgroups.
3038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C49×Dic59, C49×Dic177, C49⋊C3×Dic59 |
| maximal normal subgroup of | C3×C49×Dic59, C49⋊C3×Dic59 |
| maximal quotient of | C3×C49×Dic59, C49×Dic177 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11564, 3);