Finite Group DatabasebetaFinite Group Databasebeta| order | 242 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | Aut(G) order 1597200 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊D11 |
| Fitting, socle, derived, Sylow | C112 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 121 |
A minimal faithful permutation representation — 3 generators on 22 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);(12,13,15,17,19,21,22,20,18,16,14);(1,2,4,6,8,10,11,9,7,5,3)Polycyclic presentation:
2,11^2|b^a=b^10,c^a=c^1062 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(242, 4);