Finite Group DatabasebetaFinite Group Databasebeta| order | 1029 |
| isoclinism | isoclinic class of (C49⋊C3)⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C3)⋊C7 |
| unambiguous semidirect product | 7−1+2⋊C3 |
| Fitting, Sylow | 7−1+2 ⋊ C3 |
| derived | C49 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C49 | C3×C7 |
| Frattini, socle | C7 | C7×ΓL(1,𝔽8) |
| Fitting | 7−1+2 | C3 |
| LCS | G ▷ C49 | |
| UCS | C1 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 49 |
Polycyclic presentation:
3,7^3|b^7=d,b^a=b^2d^4,d^a=d^2,c^b=cd37 conjugacy classes — view the full character table.
| maximal subgroup of | #72215772, C2×(C49⋊C3)⋊C7, C3×(C49⋊C3)⋊C7, … |
| maximal normal subgroup of | #72215772, C2×(C49⋊C3)⋊C7, C3×(C49⋊C3)⋊C7, … |
| maximal quotient of | C2×(C49⋊C3)⋊C7, C3×(C49⋊C3)⋊C7, #72275469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1029, 14);