Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#401 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,4,6)(3,5,7,8)(9,10,12,14)(11,13,15,16)(17,18,20,21)(19,23,24,22)(25,26,27,28,29,30,31);(1,3,4,7)(2,5,6,8)(9,11)(10,13)(12,15)(14,16)(18,21)(19,24);(2,6)(5,8)(11,15)(13,16)(17,19,20,24)(18,22,21,23)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 809);