Finite Group DatabasebetaFinite Group Databasebeta| order | 11388 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#64408⋊C3 |
| unambiguous semidirect product | #64408⋊(C3×C13) |
| Fitting, socle, Hall | C13×C73 ⋊ C3×C4 |
| derived, Sylow | C73 ⋊ C3×C4×C13 |
| Hall | C13×#64408 ⋊ C3 |
| Hall | C13×C73⋊C3 ⋊ C4 |
| Hall | #64408 ⋊ C3×C13 |
| Hall | C73⋊C3 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #64408⋊C3 |
| commutator, hypocenter | C73 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C73 | C3×C4 |
| prime radical | C13×D73⋊C3 | C2 |
| cosocle | D73 | C2×C3×C13 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#14581496, #46802819, #46802820, … |
| maximal normal subgroup of | C13×#14581496, #46802819, #46802820, … |
| maximal quotient of | C13×#14581472, C3×C13×#64408⋊C3, C13×C3⋊(#64408⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11388, 26);