Finite Group DatabasebetaFinite Group Databasebeta| order | 484 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊Dic11 |
| derived, Sylow | C112 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊D11 |
| commutator, hypocenter | C112 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C112 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 484 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3,4)(6,7)(8,9)(10,11)(12,13)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26);(16,17,19,21,23,25,26,24,22,20,18);(5,6,8,10,12,14,15,13,11,9,7)Polycyclic presentation:
2^2,11^2|a^2=b,c^a=c^10,d^a=d^10124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(484, 6);