Finite Group DatabasebetaFinite Group Databasebeta| order | 11388 |
| isoclinism | isoclinic class of D73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C13×C73 ⋊ C2×C3 |
| derived, Sylow | C73 ⋊ C22×C3×C13 |
| Hall | C2×C13×D73 ⋊ C3 |
| Hall | C13×C73⋊C3 ⋊ C22 |
| Hall | C13×C73 ⋊ C22×C3 |
| Hall | C2×D73 ⋊ C3×C13 |
| Hall | C73⋊C3 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C73 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C13 | |
40 conjugacy classes of subgroups.
468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11388, 54);