Finite Group DatabasebetaFinite Group Databasebeta| order | 7018 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×D29 |
| unambiguous semidirect product | C29⋊(C2×C112) |
| Fitting, socle, Hall | C112×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D29 |
| commutator, hypocenter | C29 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C112×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C112 | |
56 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C112×#1181, C11×C11⋊#1181, C11×D11×D29, … |
| maximal normal subgroup of | C112×#1181, C11×C11⋊#1181, C11×D11×D29, … |
| maximal quotient of | C112×Dic29, C2×C112×D29, C3×C112×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7018, 6);