Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C2×C7×#126 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C7 |
| prime radical | C24×C7 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5,6,7,8,9);(10,11)(12,16)(13,14)(15,17)(18,19)(20,22)(21,23)(24,25);(11,14)(15,16)(18,20,21,24)(19,22,23,25);(1,2)(10,12,13,17)(11,15,14,16)(19,23)(22,25)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1311);