Finite Group DatabasebetaFinite Group Databasebeta| order | 11564 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×Dic49 |
| unambiguous semidirect product | C49⋊(C4×C59) |
| derived, Sylow | C49 ⋊ C4×C59 |
| Hall | C49×C59 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | D49 |
| commutator, hypocenter | C49 | C4×C59 |
| Frattini | C2×C7 | D7×C59 |
| Fitting | C2×C49×C59 | C2 |
| socle, prime radical | C2×C7×C59 | D7 |
| cosocle | C2×C49 | C2×C59 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C59 | |
18 conjugacy classes of subgroups.
3068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C59×Dic49, C59×Dic147, C59×(C49⋊C3)⋊C4 |
| maximal normal subgroup of | C3×C59×Dic49, C59×(C49⋊C3)⋊C4 |
| maximal quotient of | C3×C59×Dic49, C59×Dic147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11564, 2);