Finite Group DatabasebetaFinite Group Databasebeta| order | 7854 |
| isoclinism | isoclinic class of D187 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D187 |
| unambiguous semidirect product | C11⋊(C3×C7×D17) |
| unambiguous semidirect product | C17⋊(C3×C7×D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D187 |
| commutator, hypocenter | C11×C17 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C17 | C2 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C3×C7 | |
32 conjugacy classes of subgroups.
1995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D11×D17, C3×D7×D187, C3×D77⋊D17, … |
| maximal normal subgroup of | C3×C7×D11×D17, C3×D7×D187, C3×D77⋊D17, … |
| maximal quotient of | C3×C7×Dic187, C2×C3×C7×D187, C7×C9×D187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7854, 5);