Finite Group DatabasebetaFinite Group Databasebeta| order | 1218 |
| isoclinism | isoclinic class of C3⋊(D29⋊C7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D29⋊C7) |
| unambiguous semidirect product | D87⋊C7 |
| unambiguous semidirect product | (C29⋊C7)⋊D3 |
| Fitting, socle, derived, Hall | C3×C29 ⋊ C2×C7 |
| Hall | C3×C29⋊C7 ⋊ C2 |
| Hall | C29⋊C7 ⋊ D3 |
| Hall | D87 ⋊ C7 |
| Sylow | C29 ⋊ D3×C7 |
| Sylow | C3 ⋊ D29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C29 | C2×C7 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 87 |
Polycyclic presentation:
2,7,3,29|c^a=c^2,d^a=d^28,d^b=d^2327 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D29⋊C7, C2×C3⋊(D29⋊C7), C9⋊(D29⋊C7), … |
| maximal normal subgroup of | D3×D29⋊C7, C2×C3⋊(D29⋊C7), C3×C3⋊(D29⋊C7), … |
| maximal quotient of | C3⋊(Dic29⋊C7), C2×C3⋊(D29⋊C7), C9⋊(D29⋊C7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1218, 3);