Finite Group DatabasebetaFinite Group Databasebeta| order | 7018 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C11 |
| direct product | C29×C11⋊D11 |
| unambiguous semidirect product | C11⋊(D11×C29) |
| Fitting, socle, Hall | C112×C29 ⋊ C2 |
| derived, Sylow | C112 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C11⋊D11 |
| commutator, hypocenter | C112 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C112×C29 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C29 | |
56 conjugacy classes of subgroups.
1798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×C11⋊D11, D112×C29, (C11⋊D11)⋊D29, … |
| maximal normal subgroup of | D29×C11⋊D11, D112×C29, (C11⋊D11)⋊D29, … |
| maximal quotient of | C29×C11⋊Dic11, C2×C29×C11⋊D11, C3×C29×C11⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7018, 9);