Finite Group DatabasebetaFinite Group Databasebeta| order | 11244 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16836713 |
| Fitting, socle, Hall | C3×C937 ⋊ C4 |
| derived, Sylow | C937 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16836713 |
| commutator, hypocenter | C937 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C937 | C4 |
| prime radical | C3×D937 | C2 |
| cosocle | D937 | C2×C3 |
| LCS | G ▷ C937 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
714 conjugacy classes — view the full character table.
| maximal subgroup of | #46797995, C9×#16836713, C3×#16836713⋊C3, … |
| maximal normal subgroup of | #46797995, C9×#16836713, C3×#16836713⋊C3, … |
| maximal quotient of | C9×#16836713, C32×#16836713, C3×C3⋊#16836713 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11244, 10);