Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C11 |
| direct product | C5×C9×C11⋊D11 |
| Fitting, Hall | C5×C9×C112 ⋊ C2 |
| derived, Sylow | C112 ⋊ C2×C5×C9 |
| Hall | C9×C112 ⋊ C2×C5 |
| Hall | C5×C112 ⋊ C2×C9 |
168 conjugacy classes of subgroups.
2790 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×D112, C5×C9×#92150, C9×D5×C11⋊D11, … |
| maximal normal subgroup of | C5×C9×D112, C5×C9×#92150, C9×D5×C11⋊D11, … |
| maximal quotient of | C5×C9×C11⋊Dic11, C2×C5×C9×C11⋊D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 72);