Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C7 |
| prime radical | C7×#121 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(3,5)(4,6)(7,8)(10,13)(11,15)(17,18,19,20,21,22,23);(1,3,4,7)(2,5,6,8)(9,10,12,13)(11,14,15,16);(2,6)(5,8)(10,13)(14,16);(9,11,12,15)(10,14,13,16)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1325);