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×#125 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
226 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5,6,7,8,9);(12,16)(14,17)(18,19,21,22)(20,23,24,25);(10,11,13,15)(12,14,16,17)(19,22)(23,25);(1,2)(10,12)(11,14)(13,16)(15,17)(18,20,21,24)(19,23,22,25)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1310);