Finite Group DatabasebetaFinite Group Databasebeta| order | 462 |
| isoclinism | isoclinic class of C11⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊AGL(1,𝔽7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D11 |
| unambiguous semidirect product | D77⋊C3 |
| Fitting, socle, derived, Hall | C7×C11 ⋊ C2×C3 |
| Hall | C11×ΓL(1,𝔽8) ⋊ C2 |
| Hall | D77 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ D11 |
| Sylow | C11 ⋊ AGL(1,𝔽7) |
| Sylow | C7 ⋊ C3×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11 | C2×C3 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 77 |
A minimal faithful permutation representation — 2 generators on 18 points:
(2,5,6,3,4,7)(9,10)(11,12)(13,14)(15,16)(17,18);(1,2,4,7,6,5,3)(8,9,11,13,15,17,18,16,14,12,10)Polycyclic presentation:
2,3,7,11|c^a=c^6,d^a=d^10,c^b=c^232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(462, 3);