Finite Group DatabasebetaFinite Group Databasebeta| order | 11388 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×#64408 |
| Fitting, socle, Hall | C3×C13×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C3×C4×C13 |
| Hall | C13×C73 ⋊ C3×C4 |
| Hall | C3×C73 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | #64408 |
| commutator, hypocenter | C73 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C73 | C4 |
| prime radical | C3×C13×D73 | C2 |
| cosocle | D73 | C2×C3×C13 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3×C13 | |
24 conjugacy classes of subgroups.
858 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#14581472, #46802683, #46802684, … |
| maximal normal subgroup of | C13×#14581472, #46802683, #46802684, … |
| maximal quotient of | C9×C13×#64408, C32×C13×#64408, C3×C13×C3⋊#64408 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11388, 66);