Finite Group DatabasebetaFinite Group Databasebeta| order | 13794 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C11 |
| direct product | C3×C19×C11⋊D11 |
| unambiguous semidirect product | C11⋊(C3×C19×D11) |
| Fitting, socle, Hall | C3×C112×C19 ⋊ C2 |
| derived, Sylow | C112 ⋊ C2×C3×C19 |
| Hall | C112×C19 ⋊ C2×C3 |
| Hall | C3×C112 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | C11⋊D11 |
| commutator, cosocle, hypocenter | C112 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C19 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3×C19 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6897 |
3534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C19×#92150, C3×C19⋊#92150, C3×C19×D112, … |
| maximal normal subgroup of | C3×C19×#92150, C3×C19⋊#92150, C3×C19×D112, … |
| maximal quotient of | C3×C19×C11⋊Dic11, C2×C3×C19×C11⋊D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13794, 37);