Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×C4⋊Q8 |
| 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 | |
290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(7,8,9,10,11,12,13);(4,6)(14,15,17,19)(16,20,21,18);(1,2)(14,16,17,21)(15,18,19,20);(3,4,5,6)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1314);