Finite Group DatabasebetaFinite Group Databasebeta| order | 13805 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C251 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C251 |
| unambiguous semidirect product | C11⋊(C5×C251) |
| Fitting, socle, Hall | C11×C251 ⋊ C5 |
| derived, Sylow | C11 ⋊ C5×C251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C251 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C5×C251 |
| Frattini | C1 | G |
| Fitting, socle | C11×C251 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C251 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2761 |
1757 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊C5×C251, C11⋊C5×D251, AGL(1,𝔽11)×C251, … |
| maximal normal subgroup of | C2×C11⋊C5×C251, C11⋊C5×D251, AGL(1,𝔽11)×C251, … |
| maximal quotient of | C2×C11⋊C5×C251 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13805, 1);